# lec0314 - CS 173: Discrete Mathematical Structures Cinda...

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CS 173: Discrete Mathematical Structures Cinda Heeren [email protected] Siebe l Center, rm 2213 Office Hours: W 9:30-11:30a

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Cs173 - Spring 2004 CS 173 Announcements Homework 8 available. Due 03/26, 8a. Exam 2, Apr 4, 7-9p, Loom is 141. Email Cinda with conflicts. Today’s lecture covers material from Rosen, sections 4.4-4.5.
Cs173 - Spring 2004 CS 173 Binomial Coefficients (a + b) 2 = a 2 + 2ab + b 2 (a + b) 3 = a 3 + 3ab 2 + 3a 2 b + b 3 (a + b) 4 = a 4 + 4ab 3 + 6a 2 b 2 + 4a 3 b + b 4 Why am I showing this to you? 1. Beautiful patterns 2. Recursive defn 3. New type of proof 4. Applications in more complex counting techniques

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Cs173 - Spring 2004 CS 173 Binomial Coefficients (a + b) 2 = a 2 + 2ab + b 2 (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 (a + b) 4 = a 4 + 4a 3 b + 6a 2 b 2 + 4ab 3 + b 4 What is coefficient of a 9 b 3 in (a + b) 12 ? A. 36 B. 220 C. 15 D. 6 E. No clue
Cs173 - Spring 2004 CS 173 Binomial Coefficients (a + b) 4 = (a + b)(a + b)(a + b)(a + b) = a 4 4 0 + a 3 b 4 1 + a 2 b 2 4 2 + ab 3 4 3 + b 4 4 4 Binom ial Theorem: Let x and y be variables, and let n be any nonnegative integer. Then ( x + y ) n = n j j = 0 n x n - j y j

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Binom ial Theorem: Let x and y be variables, and let n be any nonnegative integer. Then ( x + y ) n = n j j = 0 n x n - j y j CS 173 Binomial Coefficients What is the coefficient of a 8 b 9 in the expansion of (3a +2b) 17 ? What is n?
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## This note was uploaded on 09/15/2008 for the course CS 173 taught by Professor [email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */ during the Spring '08 term at University of Illinois at Urbana–Champaign.

• Spring '08
• [email protected]

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lec0314 - CS 173: Discrete Mathematical Structures Cinda...

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