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      Question

      Find the number of ways to arrange each letter of the

      word 'AGRICULTURE' such that all the vowels always come together.
      A 60,480 Correct Answer Incorrect Answer
      B 1,25,000 Correct Answer Incorrect Answer
      C 1,51,200 Correct Answer Incorrect Answer
      D 1,77,120 Correct Answer Incorrect Answer

      Solution

      Number of letters = 11
      Take all the vowels (AIUUE) 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 = 5! ÷ 2! = 120 ÷ 2 = 60
      Required number of ways = 2,520 × 60 = 1,51,200

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