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# counting probability problem

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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:

$$\begin{array}{c|c|c} \text{Person 1} & \text{Person 2} & \text{Person 3} \\ \hline \hline \text{Seat 1} & \text{Seat 3} & \text{Seat 5} \\ \hline \text{Seat 3} & \text{Seat 5} & \text{Seat 1} \\ \hline \text{Seat 2} & \text{Seat 4} & \text{Seat 6} \end{array}$$

Nov 15, 2019