Homework 11 Quick Answers

1. 69 - C(6,1)*59 + C(6,2)*49 - C(6,3)*39 ...

2. C(52,8)- C(13,1)*C(48,4) + C(13,2)

3.SIGMA k=0,n [(-1)k * C(n,k) * 2k * (2n-1-k)!

4. 1 + 8x + 14x2 + 4x3

5. a) there's a rook in the top row or there isn't. If no rook in top row, then Rn-1,m ; if there is a rook in the top row, it can fall in any of m positions, in each case knocking out a row and a column, a adding one rook (multiplying by x) to the solution for Rn-1,m-1. For b) differentiate Rn,m with respect to x; compare the kth term of this expression with the corresponding kth term in mnRn-1,m-1 and show that they're equal using the identity given in text.

6. Assume n > m, with n containing integers 1..n. Let Ai be the condition " i belongs to chosen subset of size m". Then when you compute N(A1-bar...An-bar), which is clearly 0, you get the indicated expresson.

-- RobbieMoll - 2012-05-04

Topic revision: r7 - 2014-12-05 - RobbieMoll
 
This site is powered by the TWiki collaboration platform Powered by PerlCopyright © 2008-2019 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding UMass CS EdLab? Send feedback

mersin escort adana escort izmir escort gaziantep escort