Question

If $20$ persons are invited for a party then the number of different ways the persons and the host can be seated around 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
That can be arranged on a circular table in $18!$ ways.

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