Question

$25$ persons were invited for a party. In how many ways can they be seated in a round table such that two particular persons sit on either side of the host?

• A. $17!$
• B. $\frac{18!}{2}$
• C. $18!$
• D. $18!\times 2$

Answer 1

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

Out of the $20$ people $2$ particular people are taken out since they have a fixed place ( beside the best )

$\therefore 20-2=18$ people.

Now the host and the $2$ persons can be considered as $1$ entity. So we have to arrange $(18+1)$ people arrange the table.

This can be done in $(19-1)!=18!$

The $2$ persons sitting next to the host can interchange their places.,

$\therefore$ Total $=18!\times 2.$

Hence, the answer is $18!\times 2.$