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Quiz 2 sol - 2602Q2Ans;nb 10f2 Math 2602 Math 2602 Jan 31...

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Unformatted text preview: 2602Q2Ans;nb 10f2 Math 2602 Math 2602 Jan 31 Open Book and Notes. You have 50 minutes. Carefully explain your proceedures and answers 3111 answers should be given exactly {no decimals} if possible . Problem 1 (10 points) a) George Mallory needs to know how many ways are there to sit n people and three empty chairs arround a table of n+3 chairs, such that only relative position -—(who is to the left and right hand neighbor of each person and empty...) counts. Answer {n+3}! {n+3} 3! {n+2}! 3: Problem 2 (10 Points) Edmond Hillary would like to know how many ways there are to get (out of a 13 card hand) two threes of a kind and 2 pairs. In symbols: XXXYY-YZZW’WArBC ' Answer [1231 [1211 [31313136143 Problem 3 (10 points) Lopsang Jangbu Sherpa would like you to count the number of ways to put 10 indistiguishable balls into 5 urns, such that urn #1 does not contain more than three balls. Ans 13 If urn one contains No balls then the number of ways is [3 ) (10 balls into 4 urns) 12 If urn 1 contains 1 ball, the number of ways is [3 J (9 balls into 4 urns) 11 If urn 1 contains 2 balls,_the number of ways is [3 ] (8 balls into 4 urns) 10 If um 1 contains 3 balls, the number of ways is [3) (7 balls into 4 urns) http://www.math.gatech.edu/~morley/2602/quizes/spring02/Q2/index.htrnl 09/03/2003 11:45 PM 2602Q2Ans.nb http://wwwmath.gatech.edul~morleyl2602/quizes/sp1ing02/Q2/index.html So the ansWer is [133] + [132] + [131] + [130] Converted by Mathematica February 4, 2002 2 of 2 09/03/2003 11:45 PM I ...
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