There are $20$ chairs numbered from $1$ through $20$ around a circular table. How many ways can three people be seated, so that no two people are adjacent?
Note that these three seating arrangements are all different:
\( \begin{array}{c|c|c} \text{Person 1} & \text{Person 2} & \text{Person 3} \\ \hline \hline \text{Seat 1} & \text{Seat 3} & \text{Seat 5} \\ \hline \text{Seat 3} & \text{Seat 5} & \text{Seat 1} \\ \hline \text{Seat 2} & \text{Seat 4} & \text{Seat 6} \end{array} \)
