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.

maximum Oct 29, 2023

#1**0 **

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.

tryingtogetbetter Oct 29, 2023