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    Question

    A person has 12 friends out of which 7 are relatives. In

    how many ways can he invite 6 friends such that at least 4 of them are relatives?
    A 462 Correct Answer Incorrect Answer
    B 562 Correct Answer Incorrect Answer
    C 662 Correct Answer Incorrect Answer
    D 426 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    No. of non-relative friends = 12-7=5 He may invite 6 friends in following ways: (a). 4 relatives + 2 non-relatives = 7C 4 X 5C2 (b). 5 relatives + 1 non-relative = 7C 5 X 5C1 (c). 6 relatives + 0 non-relative = 7C 6 ∴ Reqd. no. of ways = ( 7C 4 X 5C2) + ( 7C 5 X 5C1 )+ 7C 6 = `(35xx10) + (21xx5) + 7 = 462`

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