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Permutation and Combination - General Aptitude

Q1:

In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

A 120

B 720

C 4320

D 2160

E None of these

ANS:B - 720

The word 'OPTICAL' contains 7 different letters. When the vowels OIA are always together, they can be supposed to form one letter. Then, we have to arrange the letters PTCL (OIA). Now, 5 letters can be arranged in 5! = 120 ways. The vowels (OIA) can be arranged among themselves in 3! = 6 ways.  Required number of ways = (120 x 6) = 720.