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 ?

(a) 56

(b) 896

(c) 60

(d) 768

Answer 1

Correct option is (d) 768

There are 32 black and 32 white squares on a chess board. Then number of ways of choosing one white and one black square on the chose board = ³²C₁ × ³²C₁

= 32 × 32

= 1024

There are 8 rows and 8 columns on a chess board each containing 4 white squares and 4 black squares.

∴ Number of ways to choose a white and a black square from the same row = ⁴C₁ × ⁴C₁ × 8 

= 128

Similarly, number of ways to choose a white and a black square from the same column = ⁴C₁ × ⁴C₁ × 8 

= 128

∴ Number of ways of choosing a white square and a black square on the chess board so that squares do not lie in the same row or column = 1024 – (128 + 128)

= 1024 – 256

= 768.