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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.

 

 Oct 29, 2023
 #1
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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.

 Oct 29, 2023

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