Three squares of chess board are selected at random. Find the probability of getting 2 squares of one colour and other of a different colour.

In a chess board, there are 64 squares of which 32 are white and 32 are black. Since 2 of one colour and 1 of the other can be 2W, 1B or 1W, 2B, the number of ways is (³²C₂ × ³²C₁) × 2 and also, the number of ways of choosing any 3 boxes is ⁶⁴C₃.

Hence, the required probability = ^{(32C₂ × 32C₁ × 2)}/_⁶⁴C3

= 16/21