Question

A pizza restaurant offers various kinds of toppings for you to choose from: (each topping can only be chosen at most once)

Meat: Turkey, Bacon, Pepperoni, Chicken, Meatballs

Vegetables and Fruits: Black Olives, Pineapple, Mushroom, Onion

Cheese: Mozzarella, Parmesan

a) How many pizzas with different toppings could you order if you can choose any number of the toppings available to include, including no toppings.

b) How many different pizzas could you order if you must include at least two different toppings from those available?

c) How many different pizzas could you order if you could pick any choices of meat (including none), exactly one choice of vegetables and fruits and exactly one choice of the cheese as your toppings?

Answer 1

a) There are total of 5 Meat toppings, 4 Fruits and vegetable toppings and 2 cheese toppings. Therefore total toppings possible = 5 + 4 + 2 = 11 here.

Number of different pizzas with different toppings that can be ordered given that any of toppings can be chosen including no topping is computed here as:
= Number of ways to choose each of topping^ 11 times

= 211 = 2048

Therefore there are 2048 pizzas possible here.

b) Number of pizzas possible if at least 2 toppings have to be selected

= Total ways as computed in part a) - Total ways such that there is no topping - Total ways such that there is exactly 1 topping

= 2048 - 1 - 11

= 2036

Therefore 2036 pizzas are possible here.

c) Total number of pizzas possible here:

= Total ways to select from 5 meat toppings * Total ways to choose 1 topping from 4 fruit and vegetable topping * Total ways to choose 1 cheese topping

= 25 * 4* 2

= 256

Therefore 256 pizzas are possible here.