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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 Ă— 32C3 Ă— 32C2 Ă— 32C3 / 64C5 Correct Answer Incorrect Answer
    C 2 Ă— 32C2 Ă— 32C3 / 64C5 Correct Answer Incorrect Answer
    D (32C2 + 32C3) Ă— 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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