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

Question

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

Professor PC Thomas Classes · Answer

Number of ways of arranging the letters of the word 'ASSASSIN' is $n(S)=\frac{\underline{\underline{8}}}{\underline{2\lfloor 4}}$\ (A repeats 2 times, $S$ repeats 4 times)\ Number of ways of arranging the given letters so that no two 's' comes together $n(A)=\frac{\left\lfloor\frac{4}{\lfloor 2}ight.}{}{ }^{5} C_{4}$\ Required probability\ $=P(A)=\frac{n(A)}{n(S)}=\frac{\left\lfloor\frac{4}{2} 	imes{ }^{5} C_{4}ight.}{\lfloor 2} \frac{\left\lfloor 2\left\lfloor\frac{4}{18}ight.ight.}{14}=\frac{1}{14}$\