Chessboard math

The number of ways there are to arrange 6 identical rooks on a \(10\times 10\) board such that none of them can attack each other is \(n\). Find the product of the non-zero digits of \(n\)

Details and Assumptions

A rook is a chess piece that can only move vertically and horizontally across the board. Therefore, the rooks have to be in different rows and columns of the board as each other.

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