If 20 persons were invited for a party, in how many ways will two particular persons be seated on either side of the host in a circular arrangement?
According to me the answer should be $17!.2!$. But the given answer is $18!.2!$.
If we consider the guest and the host as one unit and let them take the first three chairs the other 17 can be occupied by 17! ways and the two particular persons can then rearrange them by 2! ways.
What am i doing wrong?