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  4. 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

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Q. 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

Probability

Solution:

$A . A. I. N.$
Any $4$ of the $5$ dots can be filled with $S$. The letters $AAIN$ can be arranged in $\frac{4!}{2!}$ ways.
$\therefore $ Required probability $= \frac{^{5}C_{4} \frac{4!}{2!}}{\frac{8!}{4!\,2!}} = \frac{1}{14}$