Question

If $20$ persons are invited for a party then number of different ways the persons and the host can be seated in a circular table, if two particular persons are to be seated on either side of the host is

• A. $20!$
• B. $2\times 18!$
• C. $18!$
• D. $3!\times 18!$

Answer 1

The correct option is B $2\times 18!$

There are total of $20+1=21$ persons.
Let the two particular persons and the host be considered as one single unit.so, the remaining $21-3+1=19$ units can be arranged in circular table in $18!$ ways.

But the two persons on either side of the host can be arranged among themselves in $2!$ ways. Hence there are $2!\times 18!$ ways