In how many ways can five indistinguishable rooks be placed on an 8-by-8 chess- board so that no rook can attack another and neither the first row nor the first column is empty?

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25-08-2022
Mathematics

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In how many ways can five indistinguishable rooks be placed on an 8-by-8 chess- board so that no rook can attack another and neither the first row nor the first column is empty?

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Tundexi Tundexi · Answer 1 · 2022-08-29T12:23:33+02:00

The are 40320 ways in which the 5 indistinguishable rooks be can be placed on an 8-by-8 chess- board so that no rook can attack another and neither the first row nor the first column is empty

What involves the rook polynomial?

The rook polynomial as a generalization of the rooks problem

Indeed, its result is that 8 non-attacking rooks can be arranged on an 8 × 8 chessboard in r8.

Hence, 8! = 40320 ways.

Therefore, there are 40320 ways in which the 5 indistinguishable rooks be can be placed on an 8-by-8 chess- board so that no rook can attack another and neither the first row nor the first column is empty.