MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C9000A.578337A0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials.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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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›
̸= 9;#›
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD1wAAAAYAJQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABwAAAPwCAAD///8AAAAEAAAALQED AAQAAAAnAf//HAAAAPsC+f8AAAAAAACQAQAAAAAAQAAiQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAEAAAALQEEAAQAAAAuARgABAAAAAIBAQAFAAAACQIAAAACJQAAADIKBwAwABQAAABU cmVlcyBhbmQgRmFjdG9yaWFscwUAAgAEAAQABAACAAQABAAEAAIABAAEAAQAAgAEAAIAAgADAAIA AwAEAAAALgEAABwAAAD7AhAABwAAAAAAvAIAAAAAAQICIlN5c3RlbQAAAAAAAAAAAAAYAAAAAgAA AMDEtAfkBAAABAAAAC0BBQAEAAAA8AEEAAMAAAAAAA== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0139.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 multi-st= ep job.
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0065.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 multi-st= ep job. For example, to make a cheese omelet,
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0066.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 multi-st= ep job. For example, to make a cheese omelet, we need to (a simplified version):
 
1. get the eggs,
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0067.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 multi-st= ep 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
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0068.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 multi-st= ep 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
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0069.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 multi-st= ep 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
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0082.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,
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0092.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
The different ways the omelet j= ob may be completed can be represent by a “tree”.  <= span lang=3DEN-US style=3D'font-family:\5B8B\4F53;mso-fareast-font-family:\5B8B= \4F53; mso-hansi-font-family: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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0093.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Trees and Factorial
Trees and Factor= ials
The different ways the omelet j= ob may be completed can be represent by a “tree”.  The tree represent all possible ways of completing the three tasks abov= e.
= 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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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&= #13;
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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&= #13;
Joe
Joe
Joe
store
store
store
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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&= #13;
Joe
Joe
Joe
store
store
store
3rd step
Cook it
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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&= #13;
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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0018.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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/PhrPPngUYBAsaPIgwocKFDBs6JBiQn78OEAP2m9hgiLt9XBcxMgi1kV9Hj2jE kTyJMqXKlSxbunwJM6aBkTJv0KzJRB7JFDjD8ezpgCDQf0NLFiV6NOjNmjpPNt25VOZTj1MxVp14 1V9WfFvndU33tV3UmGHHlQV3tlvaaAUAADs= ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0018_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigBAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCF ADsAgAAAAAAAAALGTICpy+0Po5y0SnOs3rx7b3ziSJYTZqbquqHsC8dIKNf26N76ftL8D1z4gkRe roisHZPM17AJTT2jVNGyim1Ns1zKtgt+XMNk4beMPqPJ4zVb7e7C49k2nWu/1zP68rwPlQcY9TeY VGhYJJiItMioyPdY5Sj5Q1lpFInZdLlp0+mppBkKScqJaBqDmuo0yprp+noDKisVWyt6iwtDu4uj 68vSG9wxTMyxegySrKwF3Ezy9Ayt4cNMDYFxjZ1tzN2gPf19sVAAADs= ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0018_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAK AAoAgQAAAAAAAP8AAAECAwIYhINhG+KCznsKtOkQpnerPn0ec0XLURkFADs= ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0018_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwAKAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK AAoAgQAAAAAAAP8AAAECAwIXhINhG+KiznuxTYcutVrx6XUMuBzJUgAAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0018_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK ACkAgQAAAAAAAP8AAAECAwI+hBFxlyLJnHwmTNmuy1rZjoDVBDGJsqTqyrbuWqrxcqL0mdazbpvs fPv1grChryhMIpcyY8WJgAKPTWX1UAAAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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+1tJJcwoyft6TJOsqVvWjMDMl10szUUNLDKGRSQsKpawEf0JLpmOR97h fal9GIcdudYkD1qPz4OHzL55hPz988GGHEE9Bg/SupYpoMM57vw0nIhR3LmM/xxDXOwIcsLHkCSd LSyJMt/JlCRHsmTp8iXKmDJbbqwZ7F6bmzhzqtD5TmLPfwrF8Byaa9y+cm+QYmQWj6nTjPoGTsXX J2DUlVcVWUrhpmg2oF3zVMMAB2zFslG+wjhqEi7bKWcLhptbpy67u1fddtSbhibdtVMB6+plwi9e B4Z3QLtlofHiyHx/FIOllvDkHpI1XIZ8RXBSofQqR/7MFWuWWYbDPAY9E2IzRBIfp2bta+ltUllF m4OnG6TvdsSLGz+OvKpsqrsnag2+GWu65dGdr67+lzT27dy7e/8OPrz48eTLmz+PHpLc9JvSsudN /T2lDdDll65v364g/Pm/Uf8Dy19/OoAzDH1DNCcgA+049hOCDvkWyH9dkAUTYhEmk6Aal6VGYIYM prPhWBh6SAsVqIlIollWvBaLhCkilFWIlCnzokakjdPNCy7WKCKFCqiTioMejSgfhEZRRCRA2vWz 3mg0ihNaFkIiuSRMSTJm4HXqNcmWhFke6BWX4i0RoIo+pvelllSeWaRAYKJhZH9ilVgljz/GOU2d doai556tiOnnhIAGSiebhEqB56FIDKooFIk2CmOfkE5KaaWWXsoeo5jqotmmcHbqqRemhSroo6Re McOop77jwZQVgBoqFq5mAGugSsW3qKloPocrorp+94tVDP06VIehBSGsfpL/zmTsTtkku0itPl05 giqy7qUpI6U+6Wi2YYpprSuGDkktiZ3iaCGtzXr6jFYyGlXuqjut+O6x48r7qon1covvkNzkOK9i /YpUb4H8DmxDNLMG3Fmj3t5xcBLLUrrjHSwsrGjFeT3bK8JxmVYbtB4PZkk8GI+s4Ioioxwhx2+y 7NjKMKvx8swMTmxzzjrvzHPPPv8MdNAJEiv0dGoW7ZHMSCPjmtJLYwlcx0svaHLQ66L4hdOnXk3B rUdTzPUPN9x7ENH2RExnT9CcrFLDhw7CYr7xIlzbvhoDXcWJfLDtZ3IlF9y2tJn6TfadvgDOsKo1 EV74CXADfKHAnDDOd7ew/1SeuOB/4oxL40qifbPnGc/96o8163w3vDZo/bOXvB4oes/7QfSw7K9/ XbvNcGudO+qnQ435qvQ13jvKsxb/dMqxJ6988Egjz3xQzhcNffR7Ty909dbbe6nZb3E+9O+BgV/e 7lJ/ujx2u7C+pn3KfV0K+ThRfbsTk2gvS9iqZ33+t9gPS7rImA5+7ZEfOkSVukilT1kKglqQPhfA /GxEJ7apVgInBTLE9UhyI2tI3K5nwA764zWw4aDsGKPBDbrNeCkUyQX7tbYBvbBS3jMY6I4QQjvp L0IXm9kOsWQ0++EtdSHrX/YIVLXtxcVNBCzJ/761OiMyZ37s40gOzSE+Jyte8TdbnNYCn6Y5JYJF jP4io7rMeEY0HkKNa2Rjvtz4Rji6UI5zpKOzylIAADs= ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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&= #13;
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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0019.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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/q1iQV4OLuAusM7u 9f4eL99NGkBPb38/HqNvn7t8MAoaPIgwocKFDBs6fGhQ4EB/G2AokQiPIrh8WgL7aXTjJuC5jyM/ mjyJMqXKlSxbunyZsiRJjzAVpKsp4SbOIhZ38tTps4FMjUMpFvV39F5SeUvZNS33VFxUdDSDKqka dCo3rdm4WvM6DWw0sc7ILjOLDG2uAgA7 ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0019_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigBAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCF ADoAgAAAAAAAAALCTICpy+0Po5y0TmOz3rx77IXiSErGUabqmp3sC8cJKNd26N76TuX8D1zQgkTe sIis+ZJM2LEJLT2j1M+0im2hslzNtQt2LMNk8baMFp7T7DG77H6Tv3JuvG6n46v6fbTv13QXSAVI iGR4SDSoyJTY+PMIucM4GVRpCSSZqbTJ6eT5+RIqukJamoKJ2rmKuNZqdAqL8zp7I2vLoZqbisur 9UvpG3wxTGxSe2xqrGyW3Cy19gy9AcJMDXByTa09ja2lXQAAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0019_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIVBIJoFuIe2JuxzYcutjp3eUVMogAFADs= ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0019_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIZhINhF+KiznuqTVcvtRppKF0R4EHjgixAAQA7 ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0019_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK ACkAgQAAAAAAAP8AAAECAwJBhINhG+KiznuqTVcvtRppKF2RRy1HYqbqyrZstMIpqtJmgsz4jee8 zPDpgCciwPaLCZO1ZdCIfCqhzuL02qRqTQUAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0019_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8wAMAXcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADx AAoBgQAAAAAAALvg4/8AAAL/hI+py+0Po5y02otx2Ln7D4biSD6bgHLlyrbuCxsBSgtBjOf6vqpy TbvxhsSiMbFRzYC2o/MJ7SWnzFT0is0ip1NA11sVasdkHDfpQP+Y4rL7fTmrPacg/I5XyNusb/6P tccHSFhosWeYqCghuOj4iNAIObmISHlZKIm5iWfJ+Xl3BjpKxkV6mhcwsLo6iPp6pcrK6gprq8Mn OztQe+v78qU72yZY7Nv7y2AqTEtXrEl44pO8YMncOvRsjKsHhPxqejB3zdup7Xnos+R97Fe9Rfv9 eC7n1bVeIz8ZrjFNrSynShNO/P7lCBbmUkGDPHIlrOSOYSB2mSJKLGXxzcKL/xxBbOwIst+ckCTj ZCyJ0sTJlCz1rGwJU8bLmCw/0oRp82bNmTpH8dwysuevOlZUBhVKDV/RSD+R+iT2UJxTjssE6psK C5FSO1jbiZKpJGpXguiqOaQo7uhYjfVCEB0I8OtaI9BaNAWac26HshDl6k3DF1XgnoM7Fh6T1+1h wm2zMLsaYfFfvHf77MJGoe5kxX6BXS4XN/FmGJLjfCZWOavafY0ZITkd8y1kSIWnkZudtRvaZFrH 7cKtWsxWuIb5baSHPLny5czrDSdOdXXKqmKjIx1XffStQVuBa38axPt3UtLHmz+PPr369ezbu38P P778+XBS01eEz9/9Srrz7f+npMZz4v2nxRlWERgKcmBkh2BD2kCAHRsNunCOR0hIOKFJDxKRhA0D 8mafRxVqRNhvH7r0TIakXQbZiCoeRMxnoNmj2YtHyCGjcKLZWMQyOTawIY8xLKMEbBkEKWQ6R9nG IoUpJgmWfkigWN6QT8q3I21X4pKlISGegqQGF+7mSJclhWlWJAym8uV1CgoIiJnrGbhmIG3OGVad Ttzpnj/DnUiCnC++BV02fNooKGdSQlnfoYxy6OijOyQqKV2RVmrGpZiSpummwHTqqV1Vhkpqqaae iip9lKYKKaisiurqq1LEKmugq9Y66ged1QoQVzDS2mB3lgLbnjoHQrErlPf/HFvgredpwyxbxILk YlpCwFnRtKBUO4FtGM7jLGto2pUPoGUkK5K5uo57Y64A7sjdMJ9uqexHTP52JLusihLgj5TVyGtm Z/grU8CcokHOjDQCbHAF9zbZLb0NMwKxCPoaLIy6Am8jq7ZKMszloh1LXEJ+E0dGMmBqknnyx2UF GG3LtgoSs8x9IFyzzSULl7POFH7r80H+Be2gyEQfjXTSSi/NdNNOPx2qx0rnp/HS3AENtYZrYJ31 xh3qCXVyC3J9NLdm8Uw2rhd3O+bQpdLTozRVCyY1U2sjW+IwVZv9qp8VQ3j3xMEQnLLVxRAeLqPN FXQPwVSWhufic6tjZLqQ/xcnuRvXzP0vun0t/lTdZ4PctYgch+zuvoWzvbLbTN/tbdpdiy2g0aWP TihXovedJ9e7v30Wy3Zz3jKhLabeNKW/T4387Q4373zEtkefLvU7T2/989hnLz3x0S+f3vatev9e HeLHfX6wsjsGfbFQgd1s+pHfgG225OtUTM9xto9TtcvCvz/5JSVwW2idrzYBvijwrQflopsAgRIL AmbqgWVaDTJ0QcHunS5J7ljU5vaywFO1RgaOGx7pZLaQhKEmgzqziAqtdTmnvRBlG0ze35xRw+Jl DHUxxFQCcTfCYd2PQBKkg+uCVsS0GHApWRsXzAA4O2hB0Xr/Wx9JWAgmtMBZMSRY3M4WqcW/pByx f13cThgH+EMdphGFQwxbG59WxuzFkYpvlGEdMbGKqcwRFbPQ4x0fcRk/3qSPgqQJIZ2yx1HsgnsZ YIUBBsDICzgykhiYJCUtYMlLUiCTmpQAJzsJgU+C8gGiHCUDSmlKBaAylQhYJSsfmcdXOsCVr6Ql K215S0jKcpax3OUCcGlKYI5SmKAkZieNqUlkXlKZy9SlL3/Zy2e2MprShKUzq2lNbE7zmthkZiS9 yUhwfjMHBQAAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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&= #13;
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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0094.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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/q1iQV4OLuAusM7u 9f4eL99NGkBPb38/HqNvn7t8MAoaPIgwocKFDBs6fGhQ4EB/G2AokQiPIrh8WgL7aXTjJuC5jyM/ mjyJMqXKlSxbunyZsiRJjzAVpKsp4SbOIhZ38tTps4FMjUMpFvV39F5SeUvZNS33VFxUdDSDKqka dCo3rdm4WvM6DWw0sc7ILjOLDG2uAgA7 ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0094_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhigBAAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQCF ADoAgAAAAAAAAALCTICpy+0Po5y0TmOz3rx77IXiSErGUabqmp3sC8cJKNd26N76TuX8D1zQgkTe sIis+ZJM2LEJLT2j1M+0im2hslzNtQt2LMNk8baMFp7T7DG77H6Tv3JuvG6n46v6fbTv13QXSAVI iGR4SDSoyJTY+PMIucM4GVRpCSSZqbTJ6eT5+RIqukJamoKJ2rmKuNZqdAqL8zp7I2vLoZqbisur 9UvpG3wxTGxSe2xqrGyW3Cy19gy9AcJMDXByTa09ja2lXQAAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0094_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAkAgQAAAAAAAP8AAAECAwIVBIJoFuIe2JuxzYcutjp3eUVMogAFADs= ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0094_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAoAgQAAAAAAAP8AAAECAwIZhINhF+KiznuqTVcvtRppKF0R4EHjgixAAQA7 ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0094_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwArAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAK ACkAgQAAAAAAAP8AAAECAwJBhINhG+KiznuqTVcvtRppKF2RRy1HYqbqyrZstMIpqtJmgsz4jee8 zPDpgCciwPaLCZO1ZdCIfCqhzuL02qRqTQUAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0094_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8wAMAXcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADx AAoBgQAAAAAAALvg4/8AAAL/hI+py+0Po5y02otx2Ln7D4biSD6bgHLlyrbuCxsBSgtBjOf6vqpy TbvxhsSiMbFRzYC2o/MJ7SWnzFT0is0ip1NA11sVasdkHDfpQP+Y4rL7fTmrPacg/I5XyNusb/6P tccHSFhosWeYqCghuOj4iNAIObmISHlZKIm5iWfJ+Xl3BjpKxkV6mhcwsLo6iPp6pcrK6gprq8Mn OztQe+v78qU72yZY7Nv7y2AqTEtXrEl44pO8YMncOvRsjKsHhPxqejB3zdup7Xnos+R97Fe9Rfv9 eC7n1bVeIz8ZrjFNrSynShNO/P7lCBbmUkGDPHIlrOSOYSB2mSJKLGXxzcKL/xxBbOwIst+ckCTj ZCyJ0sTJlCz1rGwJU8bLmCw/0oRp82bNmTpH8dwysuevOlZUBhVKDV/RSD+R+iT2UJxTjssE6psK C5FSO1jbiZKpJGpXguiqOaQo7uhYjfVCEB0I8OtaI9BaNAWac26HshDl6k3DF1XgnoM7Fh6T1+1h wm2zMLsaYfFfvHf77MJGoe5kxX6BXS4XN/FmGJLjfCZWOavafY0ZITkd8y1kSIWnkZudtRvaZFrH 7cKtWsxWuIb5baSHPLny5czrDSdOdXXKqmKjIx1XffStQVuBa38axPt3UtLHmz+PPr369ezbu38P P778+XBS01eEz9/9Srrz7f+npMZz4v2nxRlWERgKcmBkh2BD2kCAHRsNunCOR0hIOKFJDxKRhA0D 8mafRxVqRNhvH7r0TIakXQbZiCoeRMxnoNmj2YtHyCGjcKLZWMQyOTawIY8xLKMEbBkEKWQ6R9nG IoUpJgmWfkigWN6QT8q3I21X4pKlISGegqQGF+7mSJclhWlWJAym8uV1CgoIiJnrGbhmIG3OGVad Ttzpnj/DnUiCnC++BV02fNooKGdSQlnfoYxy6OijOyQqKV2RVmrGpZiSpummwHTqqV1Vhkpqqaae iip9lKYKKaisiurqq1LEKmugq9Y66ged1QoQVzDS2mB3lgLbnjoHQrErlPf/HFvgredpwyxbxILk YlpCwFnRtKBUO4FtGM7jLGto2pUPoGUkK5K5uo57Y64A7sjdMJ9uqexHTP52JLusihLgj5TVyGtm Z/grU8CcokHOjDQCbHAF9zbZLb0NMwKxCPoaLIy6Am8jq7ZKMszloh1LXEJ+E0dGMmBqknnyx2UF GG3LtgoSs8x9IFyzzSULl7POFH7r80H+Be2gyEQfjXTSSi/NdNNOPx2qx0rnp/HS3AENtYZrYJ31 xh3qCXVyC3J9NLdm8Uw2rhd3O+bQpdLTozRVCyY1U2sjW+IwVZv9qp8VQ3j3xMEQnLLVxRAeLqPN FXQPwVSWhufic6tjZLqQ/xcnuRvXzP0vun0t/lTdZ4PctYgch+zuvoWzvbLbTN/tbdpdiy2g0aWP TihXovedJ9e7v30Wy3Zz3jKhLabeNKW/T4387Q4373zEtkefLvU7T2/989hnLz3x0S+f3vatev9e HeLHfX6wsjsGfbFQgd1s+pHfgG225OtUTM9xto9TtcvCvz/5JSVwW2idrzYBvijwrQflopsAgRIL AmbqgWVaDTJ0QcHunS5J7ljU5vaywFO1RgaOGx7pZLaQhKEmgzqziAqtdTmnvRBlG0ze35xRw+Jl DHUxxFQCcTfCYd2PQBKkg+uCVsS0GHApWRsXzAA4O2hB0Xr/Wx9JWAgmtMBZMSRY3M4WqcW/pByx f13cThgH+EMdphGFQwxbG59WxuzFkYpvlGEdMbGKqcwRFbPQ4x0fcRk/3qSPgqQJIZ2yx1HsgnsZ YIUBBsDICzgykhiYJCUtYMlLUiCTmpQAJzsJgU+C8gGiHCUDSmlKBaAylQhYJSsfmcdXOsCVr6Ql K215S0jKcpax3OUCcGlKYI5SmKAkZieNqUlkXlKZy9SlL3/Zy2e2MprShKUzq2lNbE7zmthkZiS9 yUhwfjMHBQAAOw== ------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0106.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_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0107.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
        = ;   4! =3D 4x3x2x1=3D24 etc…
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0108.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
        = ;   4! =3D 4x3x2x1=3D24 etc…
We define 0! =3D 1
Trees and Factor= ials
------=_NextPart_01C9000A.578337A0 Content-Location: file:///C:/E55611F3/4TreesandFactorials_files/slide0102.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
        = ;   4! =3D 4x3x2x1=3D24 etc…
We define 0! =3D 1