Penny's favourite pizza restaurant offers 6 toppings: ham, onions, mushrooms, pineapple, tomato and peppers. Penny ordered a pizza with ham and pineapple. Unfortunately the server only wrote down that she wanted 2 toppings but didn’t write down what they were. The cook decided to pick two toppings at random.
What is the probability that Penny will get the pizza she ordered?
Solution
Probably the most common approach is to make a list of all the possible two-topping combinations. Such a list might be organised like:
Ham and pineapple
Ham and tomatoes
Ham and peppers
Ham and mushrooms
Ham and onions
Pinepple and tomatoes
Pineapple and peppers
Pineapple and mushrooms
Pineapple and onions
Tomatoes and peppers
Tomatoes and mushrooms
Tomatoes and onions
Peppers and mushrooms
Peppers and onions
Mushrooms and onions
With the list of 15 pizzas (5 + 4 + 3 + 2 + 1) , we can easily see that Penny has a 1/15 chance of getting the pizza she ordered.
Extension
Penny actually likes all the toppings except peppers and mushrooms. What is the probability that she will get a pizza without either of these?