Question

$20$ persons are invited to a party. In how many ways can they be seated in a round table such that two particular persons sit on either side of the host?

• A. $18!\times 2$
• B. $18!\times 3$
• C. $17!\times 2$
• D. $17!\times 3$

Answer 1

Answer: (A)

$18!\times 2$

Consider the host, and the two people sitting besides him/her as one entity.

Thus, total entities become $20-2+1=19$

In a round table arrangement, the number of ways of arranging $19$ entities is $18!$

Also, in each way of arrangement, the two persons sitting beside the host can be interchanged, thus multiplying the total outcomes by $2$.

We finally get the total ways to be $18!\times 2$