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 nei

Question

Aleks04 [339]

2 years ago

13

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 nei

ther the first row nor the first column is empty?

Mathematics

1 answer:

german · Answer 1 · 2023-09-17T01:11:04+03:00

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

<h3 /><h3>What involves the rook polynomial? </h3>

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.