Question

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

• A. $\frac{1}{7}$
• B. $\frac{2}{7}$
• C. $\frac{1}{14}$
• D. $\frac{3}{14}$

Answer 1

Answer: (C)

$\frac{1}{14}$

There are 4 letters apart from the S, i.e. A, A, I, N. These may be arranged in $\frac{4!}{2!}=12$ ways. This created 5 gaps. Of these, any 4 may be chosen to place the S. This can be done in ${}^5{C}_4=5$ ways.

Required probability = $\frac{12\times 5}{\left(\frac{8!}{4!\times 2!}\right)}=\frac{60\times 4!\times 2}{8!}=\frac{1}{14}$