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    Question

    From 10 musicians and 5 singers, a band of 8 members is to

    be formed. In how many ways can the band be formed such that there are at least 6 musicians?
    A 2640 Correct Answer Incorrect Answer
    B 2700 Correct Answer Incorrect Answer
    C 2745 Correct Answer Incorrect Answer
    D 2800 Correct Answer Incorrect Answer
    E 2850 Correct Answer Incorrect Answer

    Solution

    Case I: 6 musicians and 2 singers
    Number of ways = 10C6 × 5C2 = 210 × 10 = 2100 ways
    Case II: 7 musicians and 1 singer
    Number of ways = 10C7 × 5C1 = 120 × 5 = 600 ways
    Case III: 8 musicians and 0 singers
    Number of ways = 10C8 × 5C0 = 45 × 1 = 45 ways
    Total number of ways = 2100 + 600 + 45 = 2745 ways

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