Problem 1: At the International Important Business Conference, all the seminars take place seated around round tables. Before the seminar can be- gin, each person must shake hands with exactly one other person, but to avoid awkwardness, their handshakes do not cross over each other. Some examples and a non-example are shown below for 6 business people: How many non-crossing handshake configurations (NCHCs) are there for 2n businesspeople? Come up with a recurrence relation and explain why it's true. Problem 2: Show that the non-crossing handshake configurations (NCHCS) are a Catalan object by defining and proving) a bijection between NCHCS and another Catalan object. Problem 1: At the International Important Business Conference, all the seminars take place seated around round tables. Before the seminar can be- gin, each person must shake hands with exactly one other person, but to avoid awkwardness, their handshakes do not cross over each other. Some examples and a non-example are shown below for 6 business people: How many non-crossing handshake configurations (NCHCs) are there for 2n businesspeople? Come up with a recurrence relation and explain why it's true. Problem 2: Show that the non-crossing handshake configurations (NCHCS) are a Catalan object by defining and proving) a bijection between NCHCS and another Catalan object