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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

Answer with explanation

Answer: Option BExplanation

The word ‘OPTICAL’ contains 77 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, 55 letters can be arranged in 5!=1205!=120ways. The vowels (OIA) can be arranged among themselves in 3!=63!=6 ways. Required number of ways =(120∗6)=720=(120∗6)=720.

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