Question

In how many ways can the letters of the word ‘ALGEBRA’ be arranged without changing the relative order of the vowels and consonants?

Answer 1

Given as

The word ‘ALGEBRA’

Here's 4 consonants in the word ‘ALGEBRA’

Number of ways to arrange these consonants is ⁴P₄ = 4!

There are 3 vowels in the word ‘ALGEBRA’ of which, 2 are A’s

Therefore vowels can be arranged in n!/ (p! × q! × r!) = 3! / 2! Ways

Thus, the required number of arrangements = 4! × (3! / 2!)

= [4 × 3 × 2 × 1 × 3 × 2 × 1] / (2 × 1)

= 4 × 3 × 2 × 1 × 3 = 72