Question

If the letters of the word ASSASSIN are arranged at random in row, the probability that no two S’s occur together is:

• A. $\frac{3}{5}$
• B. $\frac{1}{28}$
• C. $\frac{1}{35}$
• D. $\frac{1}{14}$

Answer 1

The correct option is D $\frac{1}{14}$

Let A, A, I, N, S, S, S, S
$✓\ast ✓\ast ✓\ast ✓\ast ✓$
Let* denotes the places for A, A, I, N then $✓$ are possible places for S.
Selection of 4 $✓$ from $5{=}^5{C}_4$
${\therefore }^5{C}_4\times \frac{4!}{2!}=60.$
Also, total number of arrangements
$\frac{8!}{4!2!}=840.$
$\therefore$ Required probability =$\frac{60}{840}=\frac{1}{14}$.