Question

If $12$ persons are seated at a round table, what is the probability that two particular persons sit together?

• A. $2/11$
• B. $1/11$
• C. $1/12$
• D. $5/12$

Answer 1

The correct option is A $2/11$

Total possible seating arrangements $=\frac{12!}{12}=11!$

If 2 persons always sit together then seating arrangements possible $=\frac{11!}{11}=10!$.

But those 2 people may interchange places $\Rightarrow$ total favourable seating arrangements$=2\times 10!$

Hence,probability $=\frac{2\times 10!}{11!}=\frac{2}{11}$