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

Question

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 (A) (1/35) (B) (1/21) (C) (1/14) (D) (1/28)

Tardigrade Admin · Accepted Answer

A . A. I. N. Any 4 of the 5 dots can be filled with S. The letters AAIN can be arranged in (4!/2!) ways. ∴ Required probability = (5C4 (4!/2!)/(8!)4! 2!) = (1/14)

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

$\frac{1}{35}$

$\frac{1}{21}$

$\frac{1}{14}$

$\frac{1}{28}$

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

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

351​

211​

141​

281​