The letters of the word ‘ASSASSIN’ are written down at random in a row. The probability that no two S occur together is

$\frac{1}{14}$

Total ways of arrangements $=\frac{8!}{2!4!}. •w•x•y•z•$

Now ‘S’ can have places at dot’s and in places of w, x, y, z we have to put 2A’s, one I and one N.

Therefore, favourable ways $= {^5C}_4 \left(\frac{4!}{2!}\right)$.

Hence, required probability $= \frac{5.4!2!4!}{2!8!}=\frac{1}{14}.$