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    Question

    From a pool of 9 science students and 5 commerce

    students, a group of 8 students is to be selected. Find the number of ways to form the group such that at least 6 science students are included.
    A 999 Correct Answer Incorrect Answer
    B 1029 Correct Answer Incorrect Answer
    C 1050 Correct Answer Incorrect Answer
    D 960 Correct Answer Incorrect Answer

    Solution

    Case I: 6 science and 2 commerce:
    9C6 ├Ч 5C2 = 84 ├Ч 10 = 840

    Case II: 7 science and 1 commerce:
    9C7 ├Ч 5C1 = 36 ├Ч 5 = 180

    Case III: 8 science and 0 commerce:
    9C8 ├Ч 5C0 = 9 ├Ч 1 = 9

    Total = 840 + 180 + 9 = 1029 ways

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