MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C957DE.B7D4C2A0" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial

This presentation contains content that your browser may not be able to = show properly. This presentation was optimized for more recent versions of Micro= soft Internet Explorer.

If you would like to proceed anyway, click here.

 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/master06.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
Click to edit Master title style
Clic= k to edit Master text styles
Sec= ond level
Thi= rd level
Fou= rth level
Fif= th level
‹date/time›
‹footer›
&#= 8249;#›
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD1QAAAAYAJQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAHAAAA/AIAAP///wAAAAQAAAAtAQMABAAA ACcB//8cAAAA+wLU/wAAAAAAAJABAAAAAABAACJBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAQAAAAtAQQABAAAAC4BGAAEAAAAAgEBAAUAAAAJAgAAAAIlAAAAMgowAC4BFAAAAFRyZWVz IGFuZCBGYWN0b3JpYWxzGgAPABkAGAAXAAwAGQAZABgADAAcABgAFgANABgADwAKABgACgAWAAQA AAAuAQAAHAAAAPsCEAAHAAAAAAC8AgAAAAABAgIiU3lzdGVtAAAAAAAAGAAAACyeEwACAAAA5AQA AAAAAAAEAAAALQEFAAQAAADwAQQAAwAAAAAA ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0139.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0140.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
We use trees to analysis events, speciffically, to count the number of possible outcomes as events unfold.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0141.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
= A job (or an experiment) that requires the completion of many steps is called a <= span lang=3DEN-US style=3D'mso-fareast-font-family:PMingLiU;mso-hansi-font-fami= ly:Arial; font-size:133%;color:red;mso-fareast-language:ZH-TW'>multi-step job= .
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
We use trees to analysis events, speciffically, to count the number of possible outcomes as events unfold.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0142.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
= A job (or an experiment) that requires the completion of many steps is called a <= span lang=3DEN-US style=3D'mso-fareast-font-family:PMingLiU;mso-hansi-font-fami= ly:Arial; font-size:133%;color:red;mso-fareast-language:ZH-TW'>multi-step job= .
For example, to make a cheese omelet, we need to
(a simplified version):
 
1. get the eggs,
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
We use trees to analysis events, speciffically, to count the number of possible outcomes as events unfold.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
= A job (or an experiment) that requires the completion of many steps is called a <= span lang=3DEN-US style=3D'mso-fareast-font-family:PMingLiU;mso-hansi-font-fami= ly:Arial; font-size:133%;color:red;mso-fareast-language:ZH-TW'>multi-step job= .
For example, to make a cheese omelet, we need to
(a simplified version):
 
1. get the eggs, <= /div>
2. get the cheese,
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
We use trees to analysis events, speciffically, to count the number of possible outcomes as events unfold.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0144.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
= A job (or an experiment) that requires the completion of many steps is called a <= span lang=3DEN-US style=3D'mso-fareast-font-family:PMingLiU;mso-hansi-font-fami= ly:Arial; font-size:133%;color:red;mso-fareast-language:ZH-TW'>multi-step job= .
For example, to make a cheese omelet, we need to
(a simplified version):
 
1. get the eggs, <= /div>
2. get the cheese, =
3. cook the omelet.
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
We use trees to analysis events, speciffically, to count the number of possible outcomes as events unfold.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0145.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
= A job (or an experiment) that requires the completion of many steps is called a <= span lang=3DEN-US style=3D'mso-fareast-font-family:PMingLiU;mso-hansi-font-fami= ly:Arial; font-size:133%;color:red;mso-fareast-language:ZH-TW'>multi-step job= .
For example, to make a cheese omelet, we need to
(a simplified version):
 
1. get the eggs, <= /div>
2. get the cheese, =
3. cook the omelet. =
 
So for the job of making a chee= se omelet may be viewed as a three-step job.
Trees and Factor= ials
= Mathematics trees are representations of structu= res of systems or events.
For instance, the file directory systems in computer storage have tree-structures.
We use trees to analysis events, speciffically, to count the number of possible outcomes as events unfold.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out. 
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0084.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0085.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0086.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0087.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0088.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store =
•<= /span>  get it from Joe, the neighbor
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0089.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store =
•<= /span>  get it from Joe, the neighbor = ;
To cook it:
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0090.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store =
•<= /span>  get it from Joe, the neighbor = ;
To cook it:
•<= /span>  do it over our stove
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0091.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store =
•<= /span>  get it from Joe, the neighbor = ;
To cook it:
•<= /span>  do it over our stove <= /span>
•<= /span>  do it over Joe’s stove
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
Thus the different ways the ome= let job may be completed can be represent by a “tree”.  <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;mso-fareast-language:ZH-CN;mso-special-format:lastCR; display:none'>
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store =
•<= /span>  get it from Joe, the neighbor = ;
To cook it:
•<= /span>  do it over our stove <= /span>
•<= /span>  do it over Joe’s stove
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
Thus the different ways the ome= let job may be completed can be represent by a “tree”.  This tree represent all possible ways of completing the three tasks above.
= Each step may have different options for how it can be carried out.  For example, to get the eggs, the options might be:
•<= /span>  get them from the frig
•<= /span>  get them from the store
•<= /span>  get them from Joe, the neighbor =
To get the cheese (assuming we = have none):
•<= /span>  get it from the store =
•<= /span>  get it from Joe, the neighbor = ;
To cook it:
•<= /span>  do it over our stove <= /span>
•<= /span>  do it over Joe’s stove
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0014.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
2nd step
Get cheese
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
2nd step
Get cheese
Joe
Joe
Joe
store
store
store
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0017.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
2nd step
Get cheese
Joe
Joe
Joe
store
store
store
3rd step
Cook it
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
2nd step
Get cheese
Joe
Joe
Joe
store
store
store
Joe
our
3rd step
Cook it
Joe
our
Joe
our
Joe
our
Joe
our
Joe
our
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhlgBsAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgCS AGcAgQAAAAAAAP8AAAECAwL/hI+py+0Po5wUhVCz3rz7dIXfSJbmE2LnyrZVqrryPF+HTef6iN/7 D5yIgsQiKmZMKgG9pRM4fEp1zanVVb1qS9Gtl5f9ijPhsTnSPash6bV7UX7L2/I6vf6O49f6vfnu d9YXKDZIuAV4+GWoeMXYKJUI6fg4uVRpmSSZ+bTJeYn0qeUpakRaSoSJ+qO6mnPqutMaWxNKqwR7 W2urWzTbe5ILzCI8HMxrLPub/FHMDPacuhy94UzNMX1NhqxNnN0tYQ1O8T1+xG1OTlduHiDwLsCe bgEPjz4vRF//fo/PhrPPngUYBAsaPIgwocKFDBs6JBiQn78OEAP2m9hgiLt9WBcxMgh1wV5Hj+Hk kTyJMqXKlSxbunwJs+XImANpbptJM4VNITp3nhPH0uRJoSSJejSKEelEpf6Y4nM6D2o6qe1w2qQ6 Dis4rd24avN6DSw1sdHIPjM7rAAAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigBAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCF ADsAgAAAAAAAAALGTICpy+0Po5y0SnOs3rx7b3ziSJYTZqbquqHsC8dIKNf26N76ftL8D1z4gkRe roisHZPM17AJTT2jVNGyim1Ns1zKtgt+XMNk4beMPqPJ4zVb7e7C49k2nWu/1zP68rwPlQcY9TeY VGhYJJiItMioyPdY5Sj5Q1lpFInZdLlp0+mppBkKScqJaBqDmuo0yprp+noDKisVWyt6iwtDu4uj 68vSG9wxTMyxegySrKwF3Ezy9Ayt4cNMDYFxjZ1tzN2gPf19sVAAADs= ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIYhINhG+KCznuqTWovzLdqCHCOcljRwqAFADs= ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KiznuxTYcutVrx6XUMuBzJUgAAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK ACkAgQAAAAAAAP8AAAECAwJAhBFxl+JqgpsCSvourhqr/SAbJE7JkpzLyrbuC7cqO6Mpfdspiex8 9GMEga6arTjsIZeypFHIxEVXT2JzejwUAAA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0018_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8wDqAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADx AOcAgQAAAAAAALvg4/8AAAL/hI+py+0Po5y02otvCELsDIbiSJbm2XDdGqDuC8ey+x3qys76zvfy VrvhPL6i8Yh8AIHDXPIJjZKW1CVAiGtJt9yuoVpbhK9NrfeMjoHHEfNXyE7L55K1GkjP6232vf+P suYGSFio0WeYqKiEuOj4+FYFOekoSHlp2Ii5uQfG+UlnBTpaGDBwOjBIuipninqqyiq75fqaOov7 JFpraybomRsMAmaLGgvx+1tJJcwoyWvck2xJW9aMwMyHXXzcNQ0sMoZFJCwqpsDbvfxtzvcx3qF+ mX0Ydx251hQPSn/Pg0dGnzxC/fz5YDNuoJ6CBqsNUZimXcOIDENJnIhxRMWM/xzr2esIcsLGkCSd QSyJ8srFlCyxrWzZciRMlDJnkqxpkx/ACjhzjoLT5qXPXAnFCB3KSpw+cm+QTmQGj6lTjPkETr3W B2DUk1cTUWOg9GGCnV0BacoAFCy4slC+vjiqVhLbt2dLrZ2LrK5OuV3dctTbCm4JwDYJ6+plwi/e uD1nQLtlwfDiyHd/FIOVQvJkunxPPMaM7+M9wV4rR74MOWXapKZd2rjMdbQ1rOB2Po49K8zWv8A6 8363FDdrsibZGT+OPLnyJcFBilYdpPlmrGNnT6ea5XpH0tq7e/8OPrz48eTLmz+PPr16LtzXP1rt /lPR+Js2SKdPyb5V/HYF3f/nz940mf0HoA7fDKNfdgVOcaCBKjwHHXHSCOiNcBlBY2Fxmi2IwWex NcihY4N46FIyIdJCBWpuSHiiF1WoaJQyLR6UFWwebTijAwWJww1niuXYmDupZBiOifQFmcIcFE4I 4TztrbJkCC0k6AGRFrHIUpQ6UrnPJEgiRSGXTmTy5HfM7fdHmeWJ2eWVTR4Jj5U/qInffChimSM6 X/ooZ55I0OlnFHsG2haghP5p6KFGDKooom82KgWjkNKI56SWXopppprGl+imlHbq6T++hYpGa6QG KOmpV4iY6qX2PTpYq4Fi0SdassKJDZqFgoreLrpWyKt3/v0aWLCFLemrdWb/3ToaiEHlqqwiozZr ZGLoiMXJtLbWymC1u8L6Xk+qbBCNg962OC2PiCGopafPaGUjYz+qWseL8YZG7x1LwOiOqfkesk2P Qcn4rwYCa3RuwQHDwm1eBJ9qbLfzHlGppu3SxULDil6cF7QKKnyjabYRCzLCysRZsrnARZsyDSuS 3LIaMMcMQ4Lg0hyrxjjvzHPPPv8MdNBCDw1nxUR3iO3RU8ystDM2MN10ZnigHLW8llAttLNj6QY1 qVrz9HLSmbJThM06k8JsyP7umhOGLie86Yj31gt3ybbN/fXQ9h6s0tl+LvcLv1s/XCDgRjv8Gt8i 1X2s4W2NpXjOEzvpOOVD/zo6uZt+v6ck4ypvziHHkV37sc+iD/40y0qHqZVANx9d1WwRx5ys2PhU fY7Hpev5etC0Lt57z69aOPu/tRaPe9+gN4087s1X/XzU0TN/ePJgBw9kscuTN7ybk/6+UPXpjdi1 i+Jz37rqnZwvbBUEkol9TAfWvvs629d3OupflA///eF7Prrq1C9b7EuS+QC4g7SlCUvqAMLlEpi3 BbXjI7cxGeEslq65xeiCLWMIifpVQNr14zOpUZ4CvaYjDW4wczz7ILs4aLd1zQmBrpoe8GDoqHxF 0GUZw9kOGaG7NumNYyNTH/Tmxz/rQSWJVKEJ14wYkviVg4kNCaFsBlgSGyriz4rUkqISTyg9//lO jEDzovW0cUaEpVGNa5QSGX9mxjTG8Yxz/GJZCgAAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
2nd step
Get cheese
Joe
Joe
Joe
store
store
store
Joe
our
3rd step
Cook it
Joe
our
Joe
our
Joe
our
Joe
our
Joe
our
FJJ
FJO
FSO
FSJ
JJO
JJJ
JSO
JSJ
SJO
SJJ
SSO
SSJ
Trees and Factor= ials
The different ways to make the omelet may be listed.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhlgBsAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgCT AGcAgQAAAAAAAP8AAAECAwL/hI+py+0Po5w0hXur3rz7b2AYSJbmCYnoyraamLnyTI8hjedmrPc+ Z/sJh48g8YgE8JJM4bIJxRmjVNezikVds9zPtAsGBsJkz7aMdnzT7MW6DQ+N43TEu56+48vnPb/v F6YX2AVIWDh3mGeoWMXYSPUI2TQ4CVVpySSZeYTJ2bn56ZQo6hha2uOJ6nO6KtXqOqMa+0obBWvL MptrRcpLhPu7EyxMslt8Qoxsprws5utcG53aPE1xbN1RnR2Bzf2y/a0GLb4S/q1iQV6+ESDwLrDO 7gUPLz/fTepeb4//PLePXzw7MAoaPIgwocKFDBs6fGhQ4Lt7/hrAUCJxYMUKWkYC9tvI0c2+cyBJ gjyJMqXKlSxbunwJU6XJkhRjipzpL53NfDp3juvpc1zQCTgrFs1Zc6gcpfmYpkiq9Cg+qfOosrNa Dqs4reigDuXKDWw2sdbITjMbDa2wAgA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigBAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCF ADoAgAAAAAAAAALCTICpy+0Po5y0TmOz3rx77IXiSErGUabqmp3sC8cJKNd26N76TuX8D1zQgkTe sIis+ZJM2LEJLT2j1M+0im2hslzNtQt2LMNk8baMFp7T7DG77H6Tv3JuvG6n46v6fbTv13QXSAVI iGR4SDSoyJTY+PMIucM4GVRpCSSZqbTJ6eT5+RIqukJamoKJ2rmKuNZqdAqL8zp7I2vLoZqbisur 9UvpG3wxTGxSe2xqrGyW3Cy19gy9AcJMDXByTa09ja2lXQAAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIWBIJoFuIe2JuxTXjuQxraG2XgkiRGAQA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIZhINhF+KiznuqTVcvtRppKF0R4EHjgixAAQA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK ACkAgQAAAAAAAP8AAAECAwJBhINhG+KiznuqTVcvtRppKF0RwIELmZzqyrZuO67xmcqIXTNJvOfH jWP5dLNfEXUcGoVAlRLJTDZpU2L0Gsw6pwUAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0019_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8wAMAXcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADx AAoBgQAAAAAAALvg4/8AAAL/hI+py+0Po5y02otx2Ln7D4biSD6bgHLlyrbuCxsBSgtBjOf6vqpy TbvxhsSiMbFRzYC2o/MJ7SWnzGb0is0ip1NA11sVasdkHDfpQP+Y4rL7fTmrPacg/I5XyNusb/6P tccHSFhosWeYqCghuOj4iNAIObmISHlZKIm5iWfJ+Xl3BjpKxkV6mhcwsLo6iPp6pcrK6gprq8Mn OztQe+v78qU72yZY7Nv7y2AqTEtXrEl4MpesJyez2zr0bIyrB4T8anowx5wduu156LP0fey3kKvr 84luvRwW/q4OTu0lV2Vlk7h+uNSwq8EP0ECC2pDgq6SPYax2mSJKHLPw3LSL/xxDZOwIMsPHkCQp jCyJ0oTFlCzhrWwJc9zLmC1P0qw58yZKmzpP5ay2sac7hBB4CrV1MAXQeUd/zUuqNFJTjvfYTAWJ CGrAq7c8BXvIlV46lw4pymQaFs7YDnVsIFublge0FkEZWYtbAm4ivXi33O36t9IRvlQDq1WFNi/h nouLMEtoV1TfCY2BYeNVYe5kj4ZdlMOsrPPmHZUPXSb202ndSaXHITkds+1Wn6JlEIMdchBUyKCy ktvFG7AYrcFhSfYXtJ7y5cybO7cHsHi+xCyrmsUq/SI5sKOdervenWFb6uH7rS6PPr369ezbu38P P778+fTrayRv/1LS7PnL6P+22h9rSkQXICRnEFjgYfWAwV2CRKBT1IANOkgChB/kAiCF+zzjmFG5 pabYNhqyBRx/oXE4omfY8GZhimbchhtyrbkYgxyXgSYjfjQascyNvYi4Y41dGBRjHCgGuaFuMA7j 2ZFBGqUkiHQ5KZ+HAnJDmpV7nWcelXGURdSVOuKEZQNPZWiIlmktxyCa95mI3oETaqHmfAYhSCeX DjK1WyBS0ijbbNr8ieRZY/ZBaKFQ1KloFIw26sSjkPKY6KQd6mmpo5VmOiimnD6x6aeijkpqqaaW J+mpD6aqqlystlpQqLDmcNysJnnqjKyfHgSnkboW2ueluO64Dp6RvlrfkMb/+vkrqs8s6x+yOrV4 1hpupiItNdRSRsy1Wzb7yIJmINSrG7XmWi4I24I6rIFW6sZkk14SO9JTK4oEpK053kBkkbblq2+S G/gYSboBmzkkwYbOeDBZ4ygcmWYNm3DvCABP7EW8sUpMKrgVzuvqoR2DbHGYGJ/IMcKReHtyBBff OWfL6P4Ts8yccaCVoDaLUGzNO1fI8s9S2CF0rEUfjXTSSi/NdNNOP91ftlCPA97ULn9nstXcCpGz wUnLGbTTbHat9LpAWVv1rGYfAibRoorbabsSSZ3Z2pk+5vW+tZnKZ8UuX2xzMBCTfPQzg9NN73PT JOxvwWXap7jcET7st68p/+8Ued49VB7i5d8qPsq5IXuutQaET+mxooCzvXLaQq++RetZlz52dCJr DTZFqcsM87W7H8xn2DKW7pLrLt1e9qa/0y458Soh73yE0EefRvPUH6858cvjbv31fmUf4PQbj5wC +B+LH77wsXTP3pk+Y8R+nGiQnWb8cRUDbUXok+mksu9HYz/jwK56snObQAKoCLsBLQjmy9P+DKWp 02XpgQlczVs0hjoJ7mlxtSgHnODWqs58BkffI93EMjJC1FDwZBFJ4cJERzuIPc+EgeMcWzSoNgzC YIAjW+H5aCgkHyYOiHSYHe9wGDuqGQ9pq+vdEq2Gjvx571/8kiLmqjMcK7KWRIjGUR92uBgOI/KP MQhECuKgBsMpTk6NRmJjG91YNzjGUY7cEsoqpgJGVMwCjw3cBDb4eJM9ApImgmxKHkexCzo+gBUG GIAiG8DIRzogkpJkACUrqYBLYhIBmtxkI+/oyUyCMpQH6KQnTblJVGJSlZVkpSRd+UhYxtKRpOTk KGspSzrmUo67hGMv3fhLNgZTjcMkJi1r+clj4vKWpCym95x5PWhST5rRo6bzrFnNHBQAADs= ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
1st step
Get eggs
frig
store
Joe
2nd step
Get cheese
Joe
Joe
Joe
store
store
store
Joe
our
3rd step
Cook it
Joe
our
Joe
our
Joe
our
Joe
our
Joe
our
FJJ
FJO
FSO
FSJ
JJO
JJJ
JSO
JSJ
SJO
SJJ
SSO
SSJ
Trees and Factor= ials
The different ways to make the omelet may be listed.
There are 3x2x2 =3D 12 ways.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhlgBsAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAgCT AGcAgQAAAAAAAP8AAAECAwL/hI+py+0Po5w0hXur3rz7b2AYSJbmCYnoyraamLnyTI8hjedmrPc+ Z/sJh48g8YgE8JJM4bIJxRmjVNezikVds9zPtAsGBsJkz7aMdnzT7MW6DQ+N43TEu56+48vnPb/v F6YX2AVIWDh3mGeoWMXYSPUI2TQ4CVVpySSZeYTJ2bn56ZQo6hha2uOJ6nO6KtXqOqMa+0obBWvL MptrRcpLhPu7EyxMslt8Qoxsprws5utcG53aPE1xbN1RnR2Bzf2y/a0GLb4S/q1iQV6+ESDwLrDO 7gUPLz/fTepeb4//PLePXzw7MAoaPIgwocKFDBs6fGhQ4Lt7/hrAUCJxYMUKWkYC9tvI0c2+cyBJ gjyJMqXKlSxbunwJU6XJkhRjipzpL53NfDp3juvpc1zQCTgrFs1Zc6gcpfmYpkiq9Cg+qfOosrNa Dqs4reigDuXKDWw2sdbITjMbDa2wAgA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigBAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCF ADoAgAAAAAAAAALCTICpy+0Po5y0TmOz3rx77IXiSErGUabqmp3sC8cJKNd26N76TuX8D1zQgkTe sIis+ZJM2LEJLT2j1M+0im2hslzNtQt2LMNk8baMFp7T7DG77H6Tv3JuvG6n46v6fbTv13QXSAVI iGR4SDSoyJTY+PMIucM4GVRpCSSZqbTJ6eT5+RIqukJamoKJ2rmKuNZqdAqL8zp7I2vLoZqbisur 9UvpG3wxTGxSe2xqrGyW3Cy19gy9AcJMDXByTa09ja2lXQAAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIWBIJoFuIe2JuxTXjuQxraG2XgkiRGAQA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIZhINhF+KiznuqTVcvtRppKF0R4EHjgixAAQA7 ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK ACkAgQAAAAAAAP8AAAECAwJBhINhG+KiznuqTVcvtRppKF0RwIELmZzqyrZuO67xmcqIXTNJvOfH jWP5dLNfEXUcGoVAlRLJTDZpU2L0Gsw6pwUAOw== ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0094_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8wAMAXcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADx AAoBgQAAAAAAALvg4/8AAAL/hI+py+0Po5y02otx2Ln7D4biSD6bgHLlyrbuCxsBSgtBjOf6vqpy TbvxhsSiMbFRzYC2o/MJ7SWnzGb0is0ip1NA11sVasdkHDfpQP+Y4rL7fTmrPacg/I5XyNusb/6P tccHSFhosWeYqCghuOj4iNAIObmISHlZKIm5iWfJ+Xl3BjpKxkV6mhcwsLo6iPp6pcrK6gprq8Mn OztQe+v78qU72yZY7Nv7y2AqTEtXrEl4MpesJyez2zr0bIyrB4T8anowx5wduu156LP0fey3kKvr 84luvRwW/q4OTu0lV2Vlk7h+uNSwq8EP0ECC2pDgq6SPYax2mSJKHLPw3LSL/xxDZOwIMsPHkCQp jCyJ0oTFlCzhrWwJc9zLmC1P0qw58yZKmzpP5ay2sac7hBB4CrV1MAXQeUd/zUuqNFJTjvfYTAWJ CGrAq7c8BXvIlV46lw4pymQaFs7YDnVsIFublge0FkEZWYtbAm4ivXi33O36t9IRvlQDq1WFNi/h nouLMEtoV1TfCY2BYeNVYe5kj4ZdlMOsrPPmHZUPXSb202ndSaXHITkds+1Wn6JlEIMdchBUyKCy ktvFG7AYrcFhSfYXtJ7y5cybO7cHsHi+xCyrmsUq/SI5sKOdervenWFb6uH7rS6PPr369ezbu38P P778+fTrayRv/1LS7PnL6P+22h9rSkQXICRnEFjgYfWAwV2CRKBT1IANOkgChB/kAiCF+zzjmFG5 pabYNhqyBRx/oXE4omfY8GZhimbchhtyrbkYgxyXgSYjfjQascyNvYi4Y41dGBRjHCgGuaFuMA7j 2ZFBGqUkiHQ5KZ+HAnJDmpV7nWcelXGURdSVOuKEZQNPZWiIlmktxyCa95mI3oETaqHmfAYhSCeX DjK1WyBS0ijbbNr8ieRZY/ZBaKFQ1KloFIw26sSjkPKY6KQd6mmpo5VmOiimnD6x6aeijkpqqaaW J+mpD6aqqlystlpQqLDmcNysJnnqjKyfHgSnkboW2ueluO64Dp6RvlrfkMb/+vkrqs8s6x+yOrV4 1hpupiItNdRSRsy1Wzb7yIJmINSrG7XmWi4I24I6rIFW6sZkk14SO9JTK4oEpK053kBkkbblq2+S G/gYSboBmzkkwYbOeDBZ4ygcmWYNm3DvCABP7EW8sUpMKrgVzuvqoR2DbHGYGJ/IMcKReHtyBBff OWfL6P4Ts8yccaCVoDaLUGzNO1fI8s9S2CF0rEUfjXTSSi/NdNNOP91ftlCPA97ULn9nstXcCpGz wUnLGbTTbHat9LpAWVv1rGYfAibRoorbabsSSZ3Z2pk+5vW+tZnKZ8UuX2xzMBCTfPQzg9NN73PT JOxvwWXap7jcET7st68p/+8Ued49VB7i5d8qPsq5IXuutQaET+mxooCzvXLaQq++RetZlz52dCJr DTZFqcsM87W7H8xn2DKW7pLrLt1e9qa/0y458Soh73yE0EefRvPUH6858cvjbv31fmUf4PQbj5wC +B+LH77wsXTP3pk+Y8R+nGiQnWb8cRUDbUXok+mksu9HYz/jwK56snObQAKoCLsBLQjmy9P+DKWp 02XpgQlczVs0hjoJ7mlxtSgHnODWqs58BkffI93EMjJC1FDwZBFJ4cJERzuIPc+EgeMcWzSoNgzC YIAjW+H5aCgkHyYOiHSYHe9wGDuqGQ9pq+vdEq2Gjvx571/8kiLmqjMcK7KWRIjGUR92uBgOI/KP MQhECuKgBsMpTk6NRmJjG91YNzjGUY7cEsoqpgJGVMwCjw3cBDb4eJM9ApImgmxKHkexCzo+gBUG GIAiG8DIRzogkpJkACUrqYBLYhIBmtxkI+/oyUyCMpQH6KQnTblJVGJSlZVkpSRd+UhYxtKRpOTk KGspSzrmUo67hGMv3fhLNgZTjcMkJi1r+clj4vKWpCym95x5PWhST5rRo6bzrFnNHBQAADs= ------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0026.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs)
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0096.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs)
A job requires the completion of k-steps.
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs)
A job requires the completion of k-steps. Suppose there are
 
N1 options to complete the 1st step
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs)
A job requires the completion of k-steps. Suppose there are
 
N1 options to complete the 1st step&#= 13;
N2 options to complete the 2nd step
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0099.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs)
A job requires the completion of k-steps. Suppose there are
 
N1 options to complete the 1st step&#= 13;
N2 options to complete the 2nd step&#= 13;
…
Nk options to complete the k’th= step
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0100.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs)
A job requires the completion of k-steps. Suppose there are
 
N1 options to complete the 1st step&#= 13;
N2 options to complete the 2nd step&#= 13;
…
Nk options to complete the k’th step
 
Then there are N1xN<= /span>2x..= xNk different ways of doing the job.
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs ):
A job requires the completion of k-steps. Suppose there are:
 
N1 options to complete the 1st step&#= 13;
N2 options to complete the 2nd step&#= 13;
…
Nk options to complete the k’th step
 
Then there are N1xN<= /span>2x..= xNk different ways of doing the job.
Trees and Factor= ials
Example A. <= /span>
A sandwich shop h= as 6 different types of bread, 4 different types of meat, 5 different types of cheese and 8
= different types of dressings.  A regular sandwich requires one of each ingredient. How many different regular sandwiches
are possible?
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0101.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Theorem (Multiplication Princip= le of Multi-step Jobs ):
A job requires the completion of k-steps. Suppose there are:
 
N1 options to complete the 1st step&#= 13;
N2 options to complete the 2nd step&#= 13;
…
Nk options to complete the k’th step
 
Then there are N1xN<= /span>2x..= xNk different ways of doing the job.
Trees and Factor= ials
Example A. <= /span>
A sandwich shop h= as 6 different types of bread, 4 different types of meat, 5 different types of cheese and 8
= different types of dressings.  A regular sandwich requires one of each ingredient. How many different regular sandwiches
are possible? = 3;
=
Ans: 6x4x5x8 =3D = 960 different sandwiches are possible.
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0061.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Factorial
Given n a positive integer, we define n factorial as
n! =3D nx(n -1)x(n – 2)x..x3x2x1 
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0103.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Factorial
Given n a positive integer, we define n factorial as
n! =3D nx(n -1)x(n – 2)x..x3x2x1 
Hence 1! =3D 1
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0104.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Factorial
Given n a positive integer, we define n factorial as
n! =3D nx(n -1)x(n – 2)x..x3x2x1 
Hence 1! =3D 1
        = ;   2! =3D 2x1=3D 2
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0105.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Factorial
Given n a positive integer, we define n factorial as
n! =3D nx(n -1)x(n – 2)x..x3x2x1 
Hence 1! =3D 1
        = ;   2! =3D 2x1=3D 2
        = ;   3! =3D 3x2x1=3D6
Trees and Factor= ials
------=_NextPart_01C957DE.B7D4C2A0 Content-Location: file:///C:/E55611F3/5TreesandFactorials_files/slide0106.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Factorial