You are given the $4 \times 4$ grid below. Find the number of ways of placing $4$ counters in the squares (at most one counter per square), so that each row contains exactly one counter, and each column contains exactly one counter.
The problem can be thought of as placing four rooks on a chessboard in a way that no two rooks can capture another.
We do this by placing the first counter on the first rank for which we have four choices. Then we have 3 choices for the second counter and so on. The answer should be 4! = 24.
Please correct me if I'm wrong.