Q. 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 persons are to be seated on either side of the host?
A) $20!$
B) $2! \times 18!$
C) $18!$
D) None of these
Explanation
(b)
There are total $20 + 1 = 21$ persons. The two particular persons and the host be taken as one unit so that these remaining $21 - 3 + 1 = 19$ persons be arranged in round table in $18!$ ways. But the two persons on either side of the host can themselves be arranged in $2!$ ways
$\therefore$ required number of ways$= 2! \times 18!$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.