Consider the following list of pizza toppings: Mushrooms, olives, peppers, pepperoni, sausage, onions, and pineapples

Question

1. How many different kinds of pizza can you order?

 

2. How many different kinds of pizza with only one topping can you order?

 

3. How many different kinds of pizza with at least one topping can you order?

 

4. How many different kinds of pizzas with at most one topping can you order?

 

5. How many different kinds of pizzas with at least two toppings can you order?

 

6. How many different kinds of pizza with at most six toppings can you order?

 

 

Answer 1

For each of the seven toppings, either the topping is on the pizza or not on the pizza - there are only two possibilities.

This can be set up as (2)(2)(2)(2)(2)(2)(2) = 2^7. So there are 128 different ways to order a pizza.

 

To answer some of the other questions think about

- how many ways can you select the first topping?

- after the first topping, how many ways can you select the second topping?

 

and so on.