Multiple choice

Consider the word $'PERMUTATION'$. How many permutations can be made with all the vowels together?

  1. $\dfrac{7!}{2!}$
  2. $7!\times 5!$
  3. $\dfrac{7!\times 5!}{2!}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
AI explanation

The word PERMUTATION contains 11 letters with T repeated twice, and it has 5 vowels along with 6 consonants. Treating the 5 vowels as a single connected unit results in 7 total units to arrange, which can be done in 7! / 2! ways because of the repeated T. The 5 vowels can be arranged within their unit in 5! ways, so the total permutations are (7! * 5!) / 2!.

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