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    Question

    Eight dancers out of which 3 are from the same team and

    the rest are solo performers have to perform in a sequence. Find the number of sequences in which all three team dancers are not performing together.
    A 37800 Correct Answer Incorrect Answer
    B 36000 Correct Answer Incorrect Answer
    C 34320 Correct Answer Incorrect Answer
    D 38400 Correct Answer Incorrect Answer
    E 40320 Correct Answer Incorrect Answer

    Solution

    Total number of arrangements = 8! = 40320 ways
    If we consider 3 team dancers as one unit, number of arrangements among themselves = 3! = 6 ways
    Number of arrangements of remaining 6 performers = 6! = 720 ways
    Therefore, required number of ways = 40320 – (6 × 720) = 36000 ways

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