1. ## Combinatorics problem

In how many ways can two rooks of different colours be put on a chessboard so that they can take each other?

2. ## Re: Combinatorics problem

So that they can or so that they cannot?

3. ## Re: Combinatorics problem

They can take each other

4. ## Re: Combinatorics problem

Put one rook on the board. There are 64 ways of doing that. regardless of where the rook is on the board, there are seven squares in the same rank and seven squares in the same file where the second rook can be such that the two rooks are attacking each other. That is $64\cdot 14$ different ways (since the two rooks are of different colors). If they are the same color, divide by 2.