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      Question

      In how many different ways can the letter of the word

      CHESTNUT is arranged so that vowels always occur together?
      A 5240 Correct Answer Incorrect Answer
      B 5140 Correct Answer Incorrect Answer
      C 5340 Correct Answer Incorrect Answer
      D 5040 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Number of letters in ‘CHESTNUT’ = 8 Number of vowels = (E, U) = 2! Number of consonants = (C, H, S, T, N, T) = 6!/2! Now, consider the number of vowels together as one and vowels can be arranged = 2! So total number of ways = (7!/2!) × 2! = 5040

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