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If the letters of the word $\text{COMPUTER}$ be arranged in random order, the number of arrangements in which the three vowels $O, U$ and $E$ occur together is

1. $8!$
2. $6!$
3. $3!6!$
4. None of these

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Answer: $\mathbf C$

Explanation:

Group the vowels together and make it a single packet $= \mathbf {OUE}$

Rest of the words are: $\mathbf {CMPTR}$

$\therefore$ Total words to be grouped including one packet $= \mathbf {\underbrace{(OUE)}_\text{=3!}CMPTR} = 6!3!$
$\therefore$ Answer $= \mathbf {3!6!}$

$\therefore \mathbf C$ is the correct option.

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