A pizza place offers the choice of the following toppings: extra cheese, mushrooms, pepperoni, ham, sausage, onions, and green peppers. Assume that each pizza must have at least 1 topping and that order of toppings is irrelevant. Also assume that toppings cannot be reused (double sausage is impossible).
a. How many 3-topping pizzas are possible?
b. If I randomly order a 3-topping pizza, what is the probability that sausage is a topping?
c. If I randomly order a 3-topping pizza, what is the probability that sausage and pepperoni are toppings?
d. Now suppose that you allow toppings to be reused. For instance, double sausage is now possible. (We have the possibility to double, triple, or even quadruple a topping, if desired.) How many different 4-topping pizzas are there?