The number of ways in which the letters of the word ‘SUCCESSFUL’ be arranged such that no two S’s will come together is

SUCCESSFUL – 10 letters [3 S’s, 2 U’s, 2 C’s, 1 E, 1 F, 1 L]

First arrange U, C, C, E, F, U, L in $\frac{7!}{2!2!}$ ways

In these letters we have 8 gaps between them

In 8 gaps 3 S’s can be arranged in $\frac{{ }^8{P}_3}{3!}$ ways

No two S’s come together

$\Rightarrow \frac{{ }^8{P}_3}{3!}\times \frac{7!}{2!2!}$.