Question:

8 rooks are randomly placed on different squares of a chessboard. A rook is said to attack all of the squares in its row and its column.

Compute the probability that every square is occupied or attacked by at least rook.

You may leave unevaluated binomial coefficients in your answer.

P.S.

I think I may have figured out the answer, which according to my calculations is (2*8^8 - 8!)/(64*63*62*61*60*59*58*57) from the Inclusion-Exclusion principle that I used in finding it. Yet I hope someone can verify my answer's correctness since I am not sure if it is accurate.

OrangeJuicy Jun 28, 2022