In how many ways is it possible to choose a white square and a black square on a chess board
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A chessboard contains white squares, so you have possible choices for the white square.
Now in the same column or row of this square lie black square which you can't choose, leaving 32 − 8 = 24 possible black squares to choose from.
This yields a total of 32 ⋅ 24 = 768 possible choices.
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