Question

Find in how many different ways the letters of a word dealing can be arranged in such a way that the vowels always come together

Answer 1

The word 'DEALING' has  

7

letters where  

3

are vowels (E, A, I).

Vowels must come together. Therefore, group these vowels and consider it as a single letter.

i.e., DLNG, (EAI)

Thus we have total  

5

different letters.?

Number of ways to arrange these  

5

letters

=

5

!

=

120

All the  

3

vowels are different.

Number of ways to arrange these  

3

vowels among themselves

=

3

!

=

6

Required number of ways

=

120

×

6

=

720