On a $7 \times 7$ chessboard, place 1 red, 1 black, and 1 white chess piece each. If the three pieces of different colors cannot be placed in the same row or column, how many different ways are there to place them?
Counting, Multiplication Principle.
First place the red piece, there are $7 \times 7=49$ squares to place it;
Then place the black piece, there are $6 \times 6=36$ squares to place it;
Finally place the white piece, there are $5 \times 5=25$ squares to place it;
By the Multiplication Principle, there are $49 \times 36 \times 25=44100$ different ways to place them.