Question

10 persons were 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. 8! x 2!
b. 9! x 2!
c. 10! x 2!
d. none of these

Answer 1

The number of ways 10 persons can be seated in a round table with two particular persons on either side of the host is 8! x 2!.

Step-by-step explanation:

To find the number of ways the 10 persons can be seated in a round table such that two particular persons sit on either side of the host, we can treat the two particular persons and the host as a combination of three people. There are 7 remaining people to be seated, so we arrange them in a straight line in 7! ways. However, since the table is round, we divide by 7 to account for the circular arrangement. The two particular persons can be arranged in 2! ways.

Therefore, the total number of ways is 7! x 2!. So the correct answer is option a. 8! x 2!