{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ex3-sol07

# ex3-sol07 - AMS 301.3(Fall 2007 Estie Arkin Exam 3 Solution...

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

AMS 301.3 (Fall, 2007) Estie Arkin Exam 3 – Solution sketch Mean 82.32, median 85, high 100 (2 of them!), low 43. 1. (20 points) Build a generating function for the the number of election outcomes in the race for class president if there are 4 candidates and 30 students votes. (You do not need to calculate the coefficient.): Each part is independent of the others! (a). Every candidate gets at least one vote? Let e i be the number of votes for candidate i , so e 1 + e 2 + e 3 + e 4 = 30, e i 1, gives the generating function g ( x ) = ( x + x 2 + x 3 + · · · ) 4 , we want the coefficient of x 30 . (b). Tiffany (one of the candidates) gets at least 4 votes? g ( x ) = (1+ x + x 2 + x 3 + · · · ) 3 ( x 4 + x 5 + · · · ), we want the coefficient of x 30 . (c). Voters are allowed to abstain (vote for none of the 4 candidates)? Let e 5 be the number of voters that abstain, we have e 1 + e 2 + e 3 + e 4 + e 5 = 30, e i 0 and so the generating function is g ( x ) = (1 + x + x 2 + x 3 + · · · ) 5 , we want the coefficient of x 30 .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}