Question

Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is.
(a) $\frac{1}{3}$

(b) $\frac{1}{6}$

(c) $\frac{2}{7}$

(d) $\frac{1}{2}$

Answer 1

If two persons sit next to eat other then consider them as 1 group
Now, we have to average 6 persons.
∴ Total number of arrangements of 7 persons is 7!
$\therefore \mathrm{Required}\mathrm{probability}=\frac{6!\times 2!}{7!}$
i.e. probability that two particular person sit next to each other is $\frac{2}{7}$.
Hence, the correct answer is option C.