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    Question

    Five articles out of which 3 are cups and rest are

    glasses have to be arranged on a shelf. Find the number of ways of arrangement in which all three cups are not placed together.
    A 96 Correct Answer Incorrect Answer
    B 84 Correct Answer Incorrect Answer
    C 102 Correct Answer Incorrect Answer
    D 72 Correct Answer Incorrect Answer
    E 108 Correct Answer Incorrect Answer

    Solution

    Since there are 5 articles, total number of ways of arrangement = 5! = 120 ways
    If we consider 3 cups as one article, number of ways of arrangement of cups among themselves = 3! = 6 ways
    Number of ways of arrangement of remaining three articles = 3! = 6 ways
    Therefore, required number of ways = 120 – (6 × 6) = 84 ways

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