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      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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