In how many different ways can the letters of the word lsquo OPTICAL rsquo be arranged so that be th...........

Quantitative Aptitude (IB) Permutation & Combination

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

120

540

720

None of these

The number of letters in the word OPTICAL is seven, in which three vowels (AIO) are considered as one.

∴ No. of ways 4 letters (PTCL) and group of three vowels which are considered as one letter can be arranged = 5!

and the no. of ways 3 vowels (AIO) can be arranged = 3!

∴ Total no. of ways = 5! × 3! = 720

Hence, option D is correct.

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