Multiple choice

In how many ways can the letters of the word ACUMEN be rearranged such that the vowels always appear together?

  1. 3!3!

  2. 6!/2!

  3. 4!.3!/2!

  4. 4!.3!

  5. 3!.3!/2!
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

ACUMEN has 6 letters: A, C, U, M, E, N. Vowels are A, U, E. Treat (AUE) as one unit. We have 4 units: (AUE), C, M, N. These can be arranged in 4! ways. The 3 vowels can be arranged within their unit in 3! ways. Total = 4! * 3!.

AI explanation

The word ACUMEN has 3 vowels and 3 consonants. Treating the 3 vowels as a single unit gives 4 total items to arrange, which can be done in 4! ways. The 3 vowels can be arranged within their own unit in 3! ways. The total number of arrangements is 4! multiplied by 3!.

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