Question

In how many ways unique can arrange the letters in the word "SUCCESSFUL"

• A. $\frac{10!}{2!2!3!}$
• B. $\frac{7!}{2!2!}{.}^8{P}_3$
• C. ${}^8{P}_3$
• D. $\frac{7!}{2!2!}.\frac{{}^8{P}_3}{3!}$

Answer 1

The correct option is A $\frac{10!}{2!2!3!}$

In the word 'SUCCESSFUL',

We have to arrange $10$ letters, out of which S occurs thrice, U and C occurs twice.

$\therefore$ Number of ways of arranging these letters $=\frac{10!}{(3!)(2!)(2!)}$

Hence the correct answer is $\frac{10!}{(3!)(2!)(2!)}$.