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  • Determine the number of different words that can be formed using the letters of the word 'DEMAND' so that the vowels are always together.  <div class='qna-optio

Determine the number of different words that can be formed using the letters of the word 'DEMAND' so that the vowels are always together.

 

Option: 1

110
 


Option: 2

150 


Option: 3

210


Option: 4

120


Answers (1)

best_answer

The word ‘DEMAND’ is made up of 6 letters.

To count the number of permutations possible when the two vowels E and A are combined.

In these cases, we group the letters that should be together and treat them as if they were one letter.

Thus, the letters are D, M, N, D, and (EA). There are now four words.

The number of ways in which the letters above can be arranged is  \frac{5!}{2!}=60\  ways.

There are two ways to arrange E and A.
Therefore, the number of ways the letters of the word 'DEMAND' can be arranged so that vowels are always together  60\times 2=120.

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Ritika Harsh

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