Choose the correct answer out of four given options in each of the exercise 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. $\frac{1}{2}$
Choose the correct answer out of four given options in each of the exercise 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. $\frac{1}{2}$

Solution:

Option (C) $2 / 7$ is correct.
Explanation:
It is given that 7 persons are to be seated in a row.
If two persons sit next to each other, then they’ll be considered as 1 group.
We now have to arrange 6 persons.
$\therefore$ No. of arrangement $=2 ! \times 6 !$
Total no. of arrangement of 7 persons $=7 !$
$\begin{array}{l}
\text { Probability }=\frac{\text { No. of favourable outcomes }}{\text { Total no. of outcomes }} \\
\therefore \text { Required probability }=\frac{2 ! \times 6 !}{7 !} \\
=\frac{2 \times 1 \times 6 !}{7 \times 6 !} \\
=\frac{2}{7}
\end{array}$
As a result, the correct option is (C).