In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

Explanation

The word INDIA has 5 letters: 3 vowels (I, I, A) and 2 consonants (N, D). There are 3 odd positions (1st, 3rd, 5th) which must be occupied by the 3 vowels. This can be done in \frac{3!}{2!} = 3 ways. The 2 consonants must occupy the remaining 2 even positions, which can be done in 2! = 2 ways. Total arrangements = 3 \times 2 = 6.

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