Handshakes

a. Five physicians gather for a meeting about a patient. If each physician shakes hands with each other physician exactly once, what is the total number of handshakes?

b. If n physicians shake hands with each other exactly once, what is the total number of handshakes?

c. How many different ways can five physicians be seated at a round table? (Assume that if everyone moves to the right, the seating arrangement is the same.)

d. How many different ways can n physicians be seated at a round table?