Random placement of rooks on a chessboard $8$ rooks are placed randomly on an $8\times 8$ chess board.
What is the probability of having exactly one rook each row and each column?
I guess there is no meaningful order here?

Hint. Eight (indistinguishable) rooks can be placed on an $8\times 8$ chess board in $\binom{64}{8}$ ways (we have to select $8$ positions among $8^2=64$).
Having exactly one rook each row and each column can be done in $8!$ ways (for each of the $8$ columns we choose e different row). 
