In how many different ways can the letters of the word ‘CANDIDATE’ be arranged in such a way that the vowels always come together

  • 4320
  • 1440
  • 720
  • 840
  • 1560
  • Explanation:

    There are 9 letters in the given word out of which 4 are vowels.

    In the word 'CANDIDATE' we treat the vowels 'AIAE'as one letter.

    Thus, we have 'CNDDT (AIAE)'

    Now, we have to arrange 6 letters, out of which D occurs twice.

    Therefore, number of ways arranging these letters = 61/21

    = 6×5×4×3×2×1/2×1=720/2=360 ways

    Now, AIAE has 4 letters in which A occurs 2 times. Number of ways of arranging these letters

    =41/21=4×3×2×1/2×1=12

    Therefore, required number of wyas

    = 360×12=4320


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In how many different ways can the letters of the word ‘CANDIDATE’ be arranged in such a
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