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      Question

      In how many different ways can the letter of the word

      ENERGY is arranged so that vowels always occur together?
      A 150 Correct Answer Incorrect Answer
      B 140 Correct Answer Incorrect Answer
      C 100 Correct Answer Incorrect Answer
      D 120 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      Number of letters in ‘ENERGY’ = 6 Number of vowels = (E, E) = 2!/2! Number of consonants = (N, R, G, Y) = 4! Now, consider the number of vowels together as one and vowels can be arranged in 2! So total number of ways = 5! × (2!/2!) = 120

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