If 20 persons were invited for a party, in how many ways can they and the host be seated at a circular table?
In how many of these ways will two particular persons be seated on either side of the host?

Explanation

To solve the problem of seating 20 persons and a host at a circular table, we can break it down into two parts:

### Part 1: Total Ways to Seat 21 Persons at a Circular Table

1. **Understanding Circular Permutations**:
When arranging \( n \) people in a circle, the number of arrangements is given by \( (n-1)! \). This is because one person can be fixed to eliminate the effect of rotations.

2. **Calculate Total Persons**:
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