A party has 20 participants. Find the number of distinct ways for the

1.	A party has 20 participants. Find the number of distinct ways for the host to sit with them around a circular table. How many of these ways have two specified persons on either side of the host?
Answer» A party has 20 participants. All of them and the host (i.e., 21 persons) can be seated at a circular table in (21 – 1)! = 20! ways. When two particular participants are seated on either side of the host. The host takes the chair in 1 way. These 2 persons can sit on either side of the host in 2! ways. Once the host occupies his chair, it is not circular permutation more The remaining 18 people occupy their chairs in 18! ways. ∴ A total number of arrangements possible if two particular participants are seated on either side of the host = 2! × 18! = 2 × 18!

A party has 20 participants. Find the number of distinct ways for the host to sit with them around a circular table. How many of these ways have two specified persons on either side of the host?

Answer»

A party has 20 participants. All of them and the host (i.e., 21 persons) can be seated at a circular table in (21 – 1)! = 20! ways.

When two particular participants are seated on either side of the host.

The host takes the chair in 1 way.

These 2 persons can sit on either side of the host in 2! ways.

Once the host occupies his chair, it is not circular permutation more

The remaining 18 people occupy their chairs in 18! ways.

∴ A total number of arrangements possible if two particular participants are seated on either side of the host = 2! × 18! = 2 × 18!