Lesson 2

Handshakes. In the problem of counting the number of ways \(H(n)\) for \(2n\) people to shake hands at a round table, we can observe the recurrence relation we need. To do so, fix one of the people at the table and consider who they could shake hands with. Relative to this handshake, the remaining pairs of people split into \(l\) and \((n-1-l)\) pairs.

Since \(H(0)=1\), we get \(H(n)=C(n)\).