OSN 2007 Problem 5

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.]