In how many ways can the letters of the word INDIA be permutated...

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