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    Question

    A committee of 5 members is to be selected from 7 men

    and 5 women. How many ways can the committee be formed if it should include at least 3 men?
    A 722 Correct Answer Incorrect Answer
    B 546 Correct Answer Incorrect Answer
    C 436 Correct Answer Incorrect Answer
    D 542 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Required number of ways: = (3 men and 2 women, 4 men and 1 woman, or 5 men and 0 woman) = ⁷C₃ × ⁵C₂ + ⁷C₄ × ⁵C₁ + ⁷C₅ × ⁵C₀ = 35 × 10 + 35 × 5 + 21 × 1 = 350 + 175 + 21 = 546

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