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    Question

    Six trophies out of which 3 are gold and the rest are

    silver are to be placed in a line. Find the number of arrangements in which all three gold trophies are not placed together.
    A 612 Correct Answer Incorrect Answer
    B 576 Correct Answer Incorrect Answer
    C 600 Correct Answer Incorrect Answer
    D 648 Correct Answer Incorrect Answer
    E 720 Correct Answer Incorrect Answer

    Solution

    Total number of ways of arrangement = 6! = 720 ways
    If we consider 3 gold trophies as one item, number of arrangements among themselves = 3! = 6 ways
    Number of arrangements of remaining 4 items = 4! = 24 ways
    Therefore, required number of ways = 720 – (6 × 24) = 576 ways

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