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    Question

    Seven musicians out of which 3 are from the same band

    and the rest are solo artists are to be seated in a row. Find the number of ways in which the three band members do not sit together.
    A 4320 Correct Answer Incorrect Answer
    B 4464 Correct Answer Incorrect Answer
    C 4176 Correct Answer Incorrect Answer
    D 5040 Correct Answer Incorrect Answer

    Solution

    Total number of arrangements = 7! = 5040 ways
    Group the 3 band members: arrangements within group = 3! = 6 ways
    Arrange 5 items = 5! = 120 ways
    Therefore, required number of ways = 5040 – (6 × 120) = 4320 ways

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