a. Five "mathletes" celebrate after solving a particularly challenging problem during competition. If each mathlete high fives each other mathlete exactly once, what is the total number of high fives?

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

c. How many different ways can five mathletes 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 mathletes be seated at a round table?