Multiple choice

The number of arrangements which can be made using all the letters of the word LAUGH if the vowels are adjacent is?

  1. $10$
  2. $24$
  3. $48$
  4. $120$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Treat vowels (A, U) as one unit. Letters are L, G, H, (AU). There are 4 units. Arrangements = 4! * 2! (for AU) = 24 * 2 = 48.

AI explanation

The word LAUGH has two vowels (A and U) and three consonants. Using the method of grouping vowels into a single block, we arrange this vowel block and the three consonants in 4 factorial ways. The two vowels can be arranged within their block in 2 factorial ways. The total number of arrangements is 4 factorial multiplied by 2 factorial, which is 24 multiplied by 2 to give 48.

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