$8$ 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 $1$ rook. you may leave unevaluated binomial coefficients in your answer. remember that if you get stuck on a homework problem, you can always ask on the message board! click on the pencil icon v in the upper-right corner of the problem, and this will open a box where you can ask your question, which will be posted on the message board. you can also click on the speech bubble icon t, which will bring up any discussions on that problem.