In how many ways can you place 32 chess pieces on a standard (8x8) chessboard? This does not have to comply with the rules of the game.
My answer is:
We place the pieces as though they all are distinguishable, i.e.
but we cannot distinguish between eight white pawns, two white knights, two white rooks, two white bishops and the same with the black ones. So the final answer is
Is my reasoning correct?