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    Question

    Six people out of which 3 are brothers and the rest are

    strangers are to be seated in a row. Find the number of ways in which all three brothers are not sitting together.
    A 576 Correct Answer Incorrect Answer
    B 648 Correct Answer Incorrect Answer
    C 720 Correct Answer Incorrect Answer
    D 504 Correct Answer Incorrect Answer
    E 600 Correct Answer Incorrect Answer

    Solution

    Total number of ways of arrangement = 6! = 720 ways
    If we consider 3 brothers as one person, number of ways of arrangement among themselves = 3! = 6 ways
    Number of ways of arrangement of remaining 4 people = 4! = 24 ways
    Therefore, required number of ways = 720 – (6 × 24) = 576 ways

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