Solution
Eight Rooks
Show the problem again
In how many ways can 8 rooks be placed on a standard 8 × 8 chessboard so that no two attack each other?
Worked solution
The answer is 40,320. Non-attacking rooks require exactly one rook per row and per column, so a placement is a bijection from rows to columns: a permutation of 8 elements. There are 8! = 40,320 such permutations.
Source: Standard non-attacking-rooks exercise from introductory combinatorics texts. Statement written for AxiomIQ.