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

Step-by-step solution

Here word 'INDIA' contains 3 vowels ( I, I, A ) and two consonants ( N , D ) Now, 3 vowels (I, I, A) can be arranged at odd position in 3! 2! =3 ways and 2 consonants ( N , D ) can be arranged in 2! ways =2 ways Hence, required number of ways =(3)(2)=6