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    Question

    A team of 6 players is to be selected from 7 men and 5

    women. In how many ways can a team be formed such that at least 4 men are included?
    A 462 Correct Answer Incorrect Answer
    B 372 Correct Answer Incorrect Answer
    C 492 Correct Answer Incorrect Answer
    D 402 Correct Answer Incorrect Answer
    E 432 Correct Answer Incorrect Answer

    Solution

    We consider possible cases where the number of men is at least 4.

    Case I: 4 men and 2 women:
    7 C 4 ├Ч 5 C 2 = 35 ├Ч 10 = 350

    Case II: 5 men and 1 woman:
    7 C 5 ├Ч 5 C 1 = 21 ├Ч 5 = 105

    Case III: 6 men and 0 women:
    7 C 6 ├Ч 5 C 0 = 7 ├Ч 1 = 7

    Total = 350 + 105 + 7 = 462 ways

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