Pizza Toppings Example

Triominoes Pizza Company specializes in 3-topping pizzas. If the available toppings are cheese, pepperoni, mushroom, pineapple and olives, how many different 3-topping combinations can customers choose from? 

This is an example of a combination problem because the order we put the toppings onto the pizza doesn't matter. 

We’ll start by making a table and list first choice, second choice and third choice:


Note that as we progress through the choices for first topping, the number of combinations we have for the second and third toppings get fewer. This is because some combinations have already been used, in a different order.

By counting the table entries we see that there are 10 possibilities for a 3-topping pizza.