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Question
In how many ways is it possible to choose a white square and a black square on a chess-board so that the squares must not lie in the same row or column?(CAT 2002)
In how many ways is it possible to choose a white square and a black square on a chess-board so that the squares must not lie in the same row or column?(CAT 2002)
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Solution
The correct option is D 768
Option (d)
There are 32 white and 32 black squares on the chessboard
Number of ways of choosing the white square = 32
When a white square is selected, we cannot select the black square lying on the row or column of the white
Square. We have 8 such black squares for every white square selected.
Hence we have 32-8=24 black squares which can be selected for every white square selected
Total number of possibilities= 32 × 24= 768. Answer is option (d)
Option (d)
There are 32 white and 32 black squares on the chessboard
Number of ways of choosing the white square = 32
When a white square is selected, we cannot select the black square lying on the row or column of the white
Square. We have 8 such black squares for every white square selected.
Hence we have 32-8=24 black squares which can be selected for every white square selected
Total number of possibilities= 32 × 24= 768. Answer is option (d)
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