qswf - MATH 239 Quiz 2 No calculators or other aids may be...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 the next 11 days. How many ways can he do this if the number of games that he plays each day is between 3 and 8? 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 ,a 11 denote the number of games that Eddie plays on days 1 through 11 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 + a 11 = n. Therefore, we need to count the number of 11-tuples whose sum is equal to n . The condition that he plays at least three, but no more than eight games every day means that 3 a i 8 for each i . The set S of all 11-tuples a 1 ,a 2 ,a 3 ,a 4 ,a 5 ,a 6 ,a 7 ,a 8 ,a 9 ,a...
View Full Document

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.

Page1 / 2

qswf - MATH 239 Quiz 2 No calculators or other aids may be...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online