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Unformatted text preview: MATH 239 Quiz 2 No calculators or other aids may be used. Show all your work. 1. Eddie plans to play n games of chess over a span of 10 days. How many ways can he do this if he plays at least one, but no more than nine games every day? Express your answer as the coefficient of a rational function (i.e. P ( x ) Q ( x ) where P ( x ) ,Q ( x ) are polynomials). You do not need to compute the coefficient explicitly. Solution. Let a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ,a 9 ,a 10 denote the number of games that Eddie plays on days 1 through 10 respectively. Then the number of ways to play n games is equal to the number of solutions to the equation a 1 + a 2 + a 3 + a 4 + a 5 + a 6 + a 7 + a 8 + a 9 + a 10 = n. Therefore, we need to count the number of 10tuples whose sum is equal to n . The condition that he plays at least one, but no more than nine games every day means that 1 ≤ a i ≤ 9 for each i . The set S of all 10tuples a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ,a 9 ,a 10 satisfying this condition is given by...
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This note was uploaded on 08/09/2009 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.
 Spring '09
 M.PEI
 Math, Combinatorics

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