# Homework Assignment 11

You may collaborate on problem numbers 3,5,6

1. How many ways are there to roll 9 distinct dice so that all 6 faces appear? [8.2.2]
2. What is the probability that an 8-card hand contains at least one "4-of-a-kind"? [8.2.4]
3. How many ways are there to seat N couples around a circular table such that no couple sits next to each other? [8.2.28]
4. Imagine a 3x3 grid with the center removed. Give the rook polynomial for this pattern [8.3.2.d]
5. [8.3.12] - same problem in editions 4,5,6. (problem 10 in edition 3)
6. Use Inclusion/Exclusion and a combinatorial argument to show that ∑k=0,m [(-1)**k C(n,k)C(n-k,m-k)] = 0.[8.2.46(b)]
Due - in class on 12/2

-- RobbieMoll - 23 Apr 2009

Topic revision: r6 - 2014-11-19 - RobbieMoll

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