Question

In how many different ways can the letters of the word $CHASE$ be arranged such that the vowels always come together.

• A. $48$
• B. $24$
• C. $12$
• D. $72$

Answer 1

The correct option is A $48$

The word $\text{CHASE}$ has $5$ letters. It has $2$ vowels $AE$ and $3$ consonants $CHS$.


We want that the two vowels $AE$ should always come together. These two vowels can be grouped together and can be considered as a single letter as $CHS\left(AE\right)$.



We can assume total letters as $4$ and these all $4$ letters are different. Number of ways of arranging $4$ letters
$=4!=4\times 3\times 2\times 1$
$=24$

We have considered the two vowels as a single letter. But these two vowels can be arrangle in $2!$ ways as $AE$ and $EA$.


Or,



Total number of ways in which letters of the word $CHASE$ can be arranged such that the two vowels always come together
$=24\times 2!=24\times 2\times 1$
$=48$

Therefore, option (a.) is the correct answer.