Question

The no. of arrangements which can be made using all the letters of the word LAUGH if the vowels are adjacent is

Answer 1

Here's your answer...

Answer 2

Given,

Word = LAUGH

Total letters in the word = 5

To Find,

The number of arrangements that can be made using the letters of the given word if the vowels are adjacent =?

Solution,

Total letters in the word LAUGH = 5

Number of vowels in the given word = 2 [a and u]

The number of ways to arrange 2 words = 2! = 2

A and U will be considered as one letter.

Now total letters = 4 [L, G, H, (A and U)]

The number of ways to arrange 4 letters  = 4!

The number of ways to arrange 4 letters  = 4 * 3 * 2 * 1

The number of ways to arrange 4 letters  =  24

Total number of ways to arrange letters of the given word if the vowels are adjacent = 24 * 2

Total number of ways to arrange letters of the given word if the vowels are adjacent = 48 ways

Hence, The number of arrangements that can be made using all the letters of the word LAUGH if the vowels are adjacent is 48.