Question

In how many ways the letters of the word "ARRANGE" can be arranged without altering the relative positions of vowels & consonants$?$

Answer 1

V$-$Vowel $,$ C$-$Consonants

Given word ARRANGE is in the form VCCVCCV.

There are $4$ consonants with $2$ same letters (R) $\xi$ $3$ vowels with $2$ same letters (A).

The vowels can be arranged in their places in $\frac{3!}{2!}$ ways $\xi$ the consonants in $\frac{4!}{2!}$ ways.

$\Rightarrow$ Total $=\frac{3!}{2!}\times \frac{4!}{2!}=36$

Hence, the answer is $36.$