20 persons are invited for a party. In how many different ways can they and the host be seated at circular table, if the two particular persona are to be seated on either side of the host?

Solution:

 There are total 20 + 1=21 persons. The two particular persons and the host be taken as one unit so that these
remains  21 -3+1=19 persons be arranged in round table in 18! ways, But the two persons on either sides of
the host can themselves be arranged in 2! ways.

Required number of ways = 2! x 18! = $2.18!$