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    Copyright © 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