Find the number of arrangements of the letters of the word ‘ALGEBRA’ without altering the relative positions of the vowels and the consonants.
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
vowel | vowel | vowel |
There are 3 spaces for vowels
There are 3 vowels out of which 2 are alike
Vowels can be placed in 
3 ways
There are 4 consonants, and they can be placed in 
= 24 ways
Total number of arrangements = 
= 72 ways
72 arrangements can be made
1