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### Discussion :: Permutation and Combination

1. 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?

2.  A. 32 B. 48 C. 36 D. 60 E. 120

Explanation :

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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