Question

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

• A. $20\mspace{6mu}!$
• B. $2\mspace{6mu}.\mspace{6mu} 18\mspace{6mu}!$
• C. $18\mspace{6mu}!$
• D. None of these

Answer 1

Answer: (B)

$2\mspace{6mu}.\mspace{6mu} 18\mspace{6mu}!$

Answer 2

There are 20 + 1 = 21 persons in all. The two particular persons and the host be taken as one unit so that these remain 21 – 3 + 1 = 19 persons to be arranged in 18 ! ways. But the two person on either side of the host can themselves be arranged in 2! ways. Hence there are 2 ! 18 ! ways or $2.18!$ ways.