Question

Seven people seat themselves indiscriminately at round table. The probability that two distinguished persons will be next to each other is

• A. $\frac{1}{3}$
• B. $\frac{1}{2}$
• C. $\frac{1}{4}$
• D. $\frac{2}{3}$

Answer 1

The correct option is A

$\frac{1}{3}$

Explanation for the correct answer:

Finding the probability that two distinguished persons will be next to each other:

We know that number of ways $n$ people can be seated around a round table$=(n-1)!$

$7$ people can be seated at a round table in $6!$ ways.

The number of ways in which two distinguished persons will be next to each other$=2\times \left(5\right)!$

Hence, the required probability is

$$\begin{gathered} \Rightarrow 2\times \frac{5!}{6!} \\ \Rightarrow 2\times \frac{5\times 4\times 3\times 2\times 1}{6\times 5\times 4\times 3\times 2\times 1} \\ \Rightarrow \frac{1}{3} \end{gathered}$$

Therefore, the correct answer is option (A).