How many ways are there to place two rooks on the same column or same row on a 8 x 8 chess board.
[Math] Enumeration problem: Two Rooks on Chess Board
combinatorics
combinatorics
How many ways are there to place two rooks on the same column or same row on a 8 x 8 chess board.
Best Answer
First imagine that the rooks have student numbers, or that one is black and the other is white.
There are $64$ ways to place the black rook. For each such way, there are $14$ ways to place the white rook, for a total of $(64)(14)$.
But the rooks are probably intended to be identical. Thus the number of black rook/white rook placements must be divided by $2$, for a total of $\frac{(64)(14)}{2}$.