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    Question

    Find the number of ways to arrange each letter of the

    word 'RECREATION' such that all the vowels always come together.
    A 10,800 Correct Answer Incorrect Answer
    B 12,000 Correct Answer Incorrect Answer
    C 18,000 Correct Answer Incorrect Answer
    D 21,600 Correct Answer Incorrect Answer

    Solution

    Number of letters = 10
    Take all the vowels (EEAIO) as one entity.
    Number of letters now = 5 + 1 = 6!
    Number of ways to arrange all the letters = 6! ÷ 2! = 720 ÷ 2 = 360
    Number of ways to arrange vowels = 5! ÷ 2! = 120 ÷ 2 = 60
    Required number of ways = 360 × 60 = 21,600

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