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

There are 4 consonants in the word 'ALGEBRA'.
The consonants are L, G, B, R. they 4 letters.
So, the number of ways to arrange these consonants = 4!
There are 3 vowels in the given word of which 2 are A'S
The vowels can be arranged among themselves in $\frac{3!}{2!}$ ways.
Hence, the required number of arrangements
=$4!\times \frac{3!}{2}$
= $4\times 3\times 2\times \frac{3\times 2}{2}$
= 72