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      Question

      In how many different ways can the letters of the word

      "AIRSTRIKE" be arranged if all the vowels must always be grouped together?
      A 720 Correct Answer Incorrect Answer
      B 1440 Correct Answer Incorrect Answer
      C 2160 Correct Answer Incorrect Answer
      D 4320 Correct Answer Incorrect Answer
      E 5040 Correct Answer Incorrect Answer

      Solution

      The word “AIRSTRIKE’’ contains 9 letters with 4 vowels, (A, 2I, 2R, S, T, K, E)

      If vowels comes together, then 4 vowels will behave as a single entity, so, remaining 5 consonants and this entity, a total of 6 letters will arrange themselves in 6! Ways, and 4 vowels will arrange themselves in

      (4!/2!) Ways, as there are 2I,

      So, total number of ways of arranging letters of the word ‘“AIRSTRIKE’’ such that all the vowels always come together = (6!/2!) × (4!/2!) = 360 × 12 = 4320

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