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    Question

    Find the number of ways to arrange each letter of the

    word 'COMMITTEE' such that all the vowels always come together.
    A 1,440 Correct Answer Incorrect Answer
    B 2,160 Correct Answer Incorrect Answer
    C 3,600 Correct Answer Incorrect Answer
    D 7,200 Correct Answer Incorrect Answer

    Solution

    Take all the vowels (OIEE) as one entity.
    Number of letters now = 5 + 1 = 6!
    Number of ways to arrange all the letters = 6! ÷ (2! × 2!) = 720 ÷ 4 = 180
    Number of ways to arrange vowels = 4! ÷ 2! = 24 ÷ 2 = 12
    Required number of ways = 180 × 12 = 2,160

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