In how many different ways can the letters of the word DRASTIC be arranged in such a way that the vowels always come together ?

There are 7 letters in the word ’DRASTIC’ including 2 vowels (A,I) and 5 consonants (D,R,S,T,C,). Considering two vowels as one letter, we have 6 letters which can be ar - ranged in 6! ways. But corresponding to each way of these arrangements, the vowels can be put together in 2! ways.

Hence, required number of words = 6! × 2!

= 720 × 2 = 1440