Question
Five squares of a chessboard are chosen at random, the
probability that three are of one colour and two of another isSolution
5 squares on a chessboard can be chosen in 64C5 ways Three squares of one colour and two squares of different colour can be chosen in two mutually exclusive ways (i) 3 white and 2 black (ii) 3 black and 2 white Thus, the favourable number of cases = 32C3 × 32C2 + 32C2 × 32C3 = 2 × 32C2 × 32C3 Required Probability = 2 × 32C2 × 32C3 / 64C5
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