There is 1 host and 20 guests, they are to be seated around a circular table.
(i) Let us fix the seat of one person, say the host, the 20 guests will be seated around the circular table in 20 ! ways, [or, (n – 1)! = (21 – 1) ! = 20!]
(ii) The two particular persons can be seated on either side of the host in 2 ways and for each way of their taking seats, the remaining 18 persons can be seated around the circular table in 18 ! ways
Hence the number of ways of seating two particular persons on either side of the host = 2 × 18 !. [or, 2! × (19 – 1)!, considering the host and two particular persons as one entity.]
