Rooks on chessboard !quiestion When I look from this perspective: My first choise ist n^2*(n-1)^2*...*1^2. The explanation is that, first i can choose from n times n position, when i have chosen one it "blocks" 1 row and 1 column. Okey obviously buy choosing my way I have n-Vector, and rooks are the same so i have to divide by n! The result would be n! And now my question if I had choosen allready a 1-set from NxN: $\binom{n^2}{1}*\binom{(n-1)^2}{1}*...*\binom{1^2}{1}$ I dont see thats is the same as n! Where is my mistake? I am counting something else, but i dont know what.

Your last expression is equal to $(n!)^2$. In the sentences leading up to it you justify that this should be divided by $n!$. It is generally true that ${a \choose 1}=a$ so the last expression is the same as your first. You just failed to divide by the $n!$