Question

How many arrangements can be made by using the letters of word $\text{ROSE}$?

• A. $24$
• B. $12$
• C. $6$
• D. $36$

Answer 1

The correct option is A $24$

There are $4$ letters in word $\text{ROSE}$.

Arrangement of letters of word $\text{ROSE}$ is same as filling four vacant places with given letters without repetition as shown.


First place can be filled in $4$ different ways by using any of letters $\text{R, O, S, E}.$
Similarly, second place can be filled in $3$ different ways.
Third place can be filled in $2$ different ways.
Fourth place can be filled in $1$ way.

So, total number of arrangements will be $4\times 3\times 2\times 1=4!=24.$