If the letters of the word ASSASSIN are written down at random in a row, the probability that no two S's occur together is

The letters of the word ASSASSIN are written down at random in a row.

A,A,S,S,S,S,I,N

n(S)=$\frac{8!}{4!2!}$

E=No two S's occur together is

$-\mathrm{A}-\mathrm{A}-\mathrm{I}-\mathrm{N}-$

Any 4 of the 5 places can be filled with S. The letters AAIN can be arranged in $\frac{4!}{2!}$ ways.In the 5 places the 4 S's can be placed in $5_{C_4}$ ways

n(E)=$\left(5_{C_4}\right)\frac{4!}{2!}$

The desired probability $=\left(5_{C_4}\right)\frac{4!}{2!}/\left(\frac{8!}{4!2!}\right)=\frac{4!5!}{8!}=\frac{1}{14}$