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.