Question

Find the number of arrangements of the letters of the word ‘ALGEBRA’ without altering the relative positions of the vowels and the consonants.

Answer 1

To find: number of arrangements without changing the relative position 

The following table shows where the vowels and consonants can be placed 

Consonants can be placed in the blank places

There are 3 spaces for vowels 

There are 3 vowels out of which 2 are alike 

Vowels can be placed in \(\frac{3!}{2!}\) = 3 ways 

There are 4 consonants, and they can be placed in = 4! = 24 ways 

⇒ Total number of arrangements = 24 x 3 = 72 ways 

72 arrangements can be made