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If the letters of the word $\textbf{COMPUTER}$ 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

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Group the vowels together and make it a single packet = $OUE$

Rest of the words are: $CMPTR$

Therefore, total words to be grouped including one packet = $(OUE)CMPTR$ = $6!$

But the packet itself can be arranged in $3!$ ways

Hence, answer = $6!3!$

So, option $C$ is the correct answer.
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