Multiple choice

What is the number of arrangements that can be made using all the letters of the word LAUGH, keeping the vowels adjacent?

  1. 120

  2. 24

  3. 48

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

The word LAUGH has 5 letters: L, A, U, G, H. Vowels are A, U. Treat (AU) as one unit. We have 4 units: {L, G, H, (AU)}. These can be arranged in 4! = 24 ways. The vowels (AU) can be arranged in 2! = 2 ways. Total = 24 * 2 = 48.

AI explanation

The word LAUGH has five distinct letters, including two vowels (A, U). Treating the two adjacent vowels as a single unit gives four total items to arrange (the vowel unit and the three consonants), which can be done in 4! ways. The two vowels within the unit can be arranged among themselves in 2! ways. Multiplying these gives 4! * 2! = 24 * 2 = 48.

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