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    Question

    Determine the total number of ways to form a committee

    consisting of 10 members from a pool of 8 men and 7 women, ensuring the committee includes at least 6 men and at least 3 women.
    A 980 Correct Answer Incorrect Answer
    B 1080 Correct Answer Incorrect Answer
    C 1260 Correct Answer Incorrect Answer
    D 1120 Correct Answer Incorrect Answer

    Solution

    Number of ways of selecting a committee with 6 men and (10 - 6) women = 8C6 X 7C4 = 28 X 35 = 980 Number of ways of selecting a committee with 7 men and 3 women = 8C7 X 7C3 = 8 X 35 = 280 So, total number of ways of forming a committee under the given conditions = 980 + 280 = 1260

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