Question 129

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

Solution

There are 7 letters in the word 'DRASTIC' including 2 vowels (A,I) and 5 consonants (D,R,S,T,C).

Considering the two vowels as 1 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.

Hence, required number of words = $$6! \times 2!$$

= 720 * 2 = 1440

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