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      Question

      Find the number of ways to arrange each letter of the

      word 'RECREATION' such that all the vowels always come together.
      A 10,800 Correct Answer Incorrect Answer
      B 12,000 Correct Answer Incorrect Answer
      C 18,000 Correct Answer Incorrect Answer
      D 21,600 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Word: RECREATION Letters: R, E, C, R, E, A, T, I, O, N Vowels: E, E, A, I, O Consonants: R, R, C, T, N Step 1: Treat all vowels as one block Items to arrange → [VOWELS], R, R, C, T, N Total = 6 items, R repeated twice Ways = 6! / 2! = 720 / 2 = 360 Step 2: Arrange the vowels inside the block Vowels → E, E, A, I, O Total = 5 letters, E repeated twice Ways = 5! / 2! = 120 / 2 = 60 Step 3: Total arrangements Total = 360 × 60 = 21,600

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