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There are $$20$$ people around a table. Each person shakes hands with the person immediately to the left and the person immediately to the right. The total number of handshakes is
Each person has two neighbouring handshakes, giving $$20 \times 2=40$$ counts. Every handshake is counted twice, once by each participant. Therefore, the number of distinct handshakes is $$\frac{40}{2}=20$$.
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