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    Question

    From a group of 8 engineers and 4 doctors, a committee of 6

    members is to be formed. Find the number of ways to form the committee such that at least 5 engineers are selected.
    A 224 Correct Answer Incorrect Answer
    B 256 Correct Answer Incorrect Answer
    C 196 Correct Answer Incorrect Answer
    D 252 Correct Answer Incorrect Answer
    E 268 Correct Answer Incorrect Answer

    Solution

    Case I: 5 engineers and 1 doctor:
    8 C 5 × 4 C 1 = 56 × 4 = 224

    Case II: 6 engineers and 0 doctors:
    8 C 6 × 4 C 0 = 28 × 1 = 28

    Total = 224 + 28 = 252 ways

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