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    Question

    Five different pens out of which 2 are red and the rest

    are blue are to be arranged in a line. Find the number of ways in which the two red pens are not placed together.
    A 96 Correct Answer Incorrect Answer
    B 84 Correct Answer Incorrect Answer
    C 72 Correct Answer Incorrect Answer
    D 60 Correct Answer Incorrect Answer

    Solution

    Total number of ways to arrange 5 pens = 5! = 120 ways
    If we consider 2 red pens as one item, number of arrangements = 2! = 2 ways
    Number of arrangements of remaining 4 items = 4! = 24 ways
    Therefore, required number of ways = 120 – (2 × 24) = 72 ways

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