[720] In how many different ways can the letters of the word OPTICAL be arranged so that the vowels always

For Competitive Exams

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

120

720

4320

2160

Explanation:

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.

$\therefore$ Required number of ways = $\left(120 \times 6\right)$ = 720.

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