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In how many ways can all the letters of the word TANI be arranged so that vowels remain together?

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There are 4 letters in the word TANI of which 2 vowels are A and I.

Considering 2 vowels as 1 letter, total (2 + 1) = 3 letters can be arranged in 3P3 ways and in each of these arrangements two vowels can be arranged among themselves in 2P2 ways.

Total permutations = 3P3 × 2P2

= 3! × 2!

= 6 × 2 = 12

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