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

Consider the problem

In the word $ALGEBRA$, there are three Vowels $(A,AandE)$ and four Consonants $(L,G,BandR)$

We need to find the different arrangements of the word $ALGEBRA$ such that relative positions of Vowels and Consonants do not change.

Therefore, in the three positions occupied by vowels, we can rearrange the vowels in $\frac{3!}{2!}=3ways$

And, four consonants can be rearranged in four spaces occupied by consonants in $4!ways=24ways$

Therefore, required number of arrangements

$=3\times 24=72$