Here is a tricky counting problem.

"How many ways can two red and four blue rooks be placed on an 8-by-8 chessboard so that no two rooks can attack one another?".

I believe that all placements of 6 non-attacking rooks on the board would be

$\displaystyle (C(8,6))^{2}\cdot 6!$, but the two different colors are tricky. Or am I making it too difficult?.