Question

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

• A. 720
• B. 360
• C. 1440
• D. 540
• E. None of these

Answer 1

The correct option is C 1440

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 arranged in 6! ways. But corresponding to each way of these arrangements, the vowels can be put together in 2! ways.
By short Trick 2
Here, m= 2, n = 7
$\therefore$ Number of arrangements
= m! (n - m + 1)! = 2! (7 - 2 + 1)! = 2! $\times$ 6!
$=6\times 5\times 4\times 3\times 2\times 1\times 2\times 1=1440$