Question

In how many ways can ve distinguishable (distinct) rooks be placed on an 8-by-8 chess- board so that no rook can attack another and neither the rst row nor the rst column is empty?

Answer 1

Step-by-step explanation:

40320

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 = 8! = 40320 ways.