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Answer :

42Solution :

The word 'INDIA' contains 2 I's, 1 A, 1 N and 1 D. <br> Number of permutations of the letters of the given word `=(5!)/(2!)=60.` <br> Let us assume that the vowels IIA form 1 letter. <br> Now, IIA + ND gives 3 letters, all district. <br> Number of their arrangements = 3! = 6. <br> Now, IIA has 3 letters, out of which there are 2 I's and 1 A. <br> Number of their arrangements `=(3!)/(2!)=3.` <br> Number of words having all vowels together `=(6xx3)=18.` <br> Number of words in which all vowels are not together `=(60-18)=42.`