Question

    Find the number of ways to arrange each letter of the

    word 'PROFESSION' such that all the vowels always come together.
    A 24,000 Correct Answer Incorrect Answer
    B 28,800 Correct Answer Incorrect Answer
    C 30,240 Correct Answer Incorrect Answer
    D 32,400 Correct Answer Incorrect Answer

    Solution

    Number of letters = 10
    Take all the vowels (OEIO) as one entity.
    Number of letters now = 6 + 1 = 7!
    Number of ways to arrange all the letters = 7! ÷ 2! = 5040 ÷ 2 = 2,520
    Number of ways to arrange vowels = 4! ÷ 2! = 24 ÷ 2 = 12
    Required number of ways = 2,520 × 12 = 30,240

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