Question

In how many ways is it possible to choose a white square and a black square on a chessboard so that the squares must not lie in the same row or column?

• A. 56
• B. 896
• C. 60
• D. 768

Hint:

When selecting items from a grid with restrictions, subtract the number of choices available in the same row or column.

Answer 1

The Correct Option is D

A chessboard has 8 rows and 8 columns. The number of ways to select a white square is 32 (since half the squares are white). Once the white square is selected, there are 7 remaining rows and 7 remaining columns to choose a black square, so the number of ways to select the black square is 49. Thus, the total number of ways is: \[ 32 \times 49 = 768. \] Therefore, the Correct Answer is 768.