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

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