In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

LohaHridoy
  1. 32
  2. 48
  3. 36
  4. 60
  5. 120

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Answer: Option 3

There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants. Let us mark these positions as under: (1) (2) (3) (4) (5) (6) Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5 Number of ways of arranging the vowels = 3P3 = 3! = 6 Also, the 3 consonants can be arranged at the remaining 3 positions. Number of ways of these arrangements = 3P3 = 3! = 6 Total number of ways = (6 x 6) = 36

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