Question

The number of arrangements that can be made out of the letters of the word $SUCCESS$ so that all $S$ do not come together is

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

Answer 1

Answer: (C)

$360$

Total together of 7 (3 S's, 2 c's, 2 different) letters $=\frac{7!}{3!2!}$

Total together with 2 C's in which 3 S's come together $=\frac{5!}{2!}$

Thus, total in which 3 S's do not come together $=\frac{7!}{2!3!}-\frac{5!}{2!}=\frac{5!}{2!}(\frac{42}{6}-1)=360$