Counting orders at a restaurant.

A group of five friends go to a restaurant for dinner. The restaurant offers 20 different main dishes.

(a)

Suppose that the group collectively orders five different dishes to share. The waiter just needs to place all five dishes in the center of the table. How many different possible orders are there for the group?

(b)

Suppose that each individual orders a main course. The waiter must remember who ordered which dish as part of the order. It's possible for more than one person to order the same dish. How many different possible orders are there for the group?

(c)

Suppose that each individual orders a main course. The waiter must remember who ordered which dish as part of the order. However the friends agree that no two people will order the same dish.