Question 45

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?

Solution

First a black square can be selected in 32 ways. Out of remaining rows and columns, 24 white squares remain. 1 white square can them be chosen in 24 ways. So total no. of ways of selection is 32*24 = 768.

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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?

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