Let r, s be two positive integers and P a 'chessboard' with r rows and s columns. Let M denote the maximum value of rooks placed on P such that no two of them attack each other.
(a) Determine M.
(b) How many ways to place M rooks on P such that no two of them attack each other?
[Note: In chess, a rook moves and attacks in a straight line, horizontally or vertically.] combinatorics proposedcombinatorics