Competition problem — Combinatorics

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Combinatorics Difficulty 6.5 National olympiad Prove it

Example 2
Given $p(p \geq 5)$ is a prime number. From a $p \times p$ chessboard, choose $p$ squares such that the chosen squares are not all in the same row (they can be in the same column), and let the number of such selections be $r$ . Prove: $p^{5} \mid r$ .

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.