Permutations and Combinations

1. in how many ways can five identical rooks be placed on the squares of an 8 by 8 board so that four of them forma the corners of a rectangle with sides parallel to the sides of the board. 2. consider and 9 by 9 board and nine rooks of which five are red and four are blue. suppose you place the rooks on the board in nonattac ...continues

Generating Permutations and Combinations

a.Consider the partial order less than or equal to(<=) on the set X of positive integers given by "is a divisor of." Let a and b be two integers. Let c be the largest integer such that c<=a and c<=b and let d be the smallest integer such that a<=d and b<=d. What are c and d? b. Prove that the intersection of R and S of two eq ...continues