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Question

Five squares of a chessboard are chosen at random, the probability that three are of one colour and two of another is

A (32C2 + 32C3) / 64C5 Correct Answer Incorrect Answer
B 32C2 × 32C3 × 32C2 × 32C3 / 64C5 Correct Answer Incorrect Answer
C 2 × 32C2 × 32C3 / 64C5 Correct Answer Incorrect Answer
D (32C2 + 32C3) × 2 / 64C5 Correct Answer Incorrect Answer
E None of these Correct Answer Incorrect Answer

Solution

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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