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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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1 Answer

+2 votes

Answer: $\mathbf C$


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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