Question

The number of arrangements that can be made out of the letter of the word "SUCCESS" so that the all S's do not come together is?

• A. $60$
• B. $120$
• C. $360$
• D. $420$

Answer 1

The correct option is C

$360$

Explanation for correct option

There are $7$ letter in the word “ SUCCESS ”

There are $3$ S's, $2$C's and $2$ different alphabet

So,

Total number of arrangement $=\frac{7!}{3!2!}$

Total arrangement with $2$C' where $3$ S's comes together $\frac{5!}{2!}$

Therefore total arrangement when $3$ S's do not come together $=\frac{7!}{3!2!}-\frac{5!}{2!}=360$

Hence, the correct option is $\left(\mathrm{C}\right)$.