# Lesson Worksheet: Counting Outcomes Mathematics

In this worksheet, we will practice counting outcomes using tree diagrams and the fundamental counting principle.

**Q1: **

Michel, Kayla, and ChiWei are playing a game, where one of them needs to be a sheriff and one needs to be an outlaw. They write each of their names on a piece of paper and place them in a bowl. If two names are picked at random where the first will be a sheriff and the second will be an outlaw how many different ways are there?

**Q2: **

A pizza parlor offers customizable pizzas. Customers can choose one of two options for the base, cheese, and sauce and then add an optional topping.

Base | Cheese | Sauce | Topping (at Most One) |
---|---|---|---|

Thin crust or deep pan | Cheddar or mozzarella | Tomato or barbecue | Pepperoni, pineapple, or mushroom |

Using tree diagrams, or otherwise, represent all the possible pizza combinations and determine how many different pizzas there are.

**Q3: **

An ice cream store offers 3 different cup sizes and 14 flavors. How many ways are there to buy a single flavor of ice cream?

**Q4: **

A coin is flipped 3 times. Use the following tree diagram to determine the event that includes all of the outcomes where no more than two tails are flipped.

- A
- B
- C
- D

**Q5: **

A coin is flipped three consecutive times. Which of the following represents the event of getting a head on the first flip?

- A
- B
- C
- D

**Q6: **

A cafe offers a choice of 20 meals and 9 beverages. In how many different ways can a person choose a meal and a beverage?

**Q7: **

A restaurant serves 2 types of pie, 4 types of salad, and 3 types of drink. How many different meals can the restaurant offer if a meal includes one pie, one salad, and one drink?

**Q8: **

In how many ways can a 5-digit code be formed using the numbers 1 to 9? Note, the code can have repeated digits.

**Q9: **

A school gives three prizes for excellence. The short lists for the prizes contain 9 students, 7 students, and 6 students. In how many ways can the prizes be distributed?

**Q10: **

A car dealership offers 73 different models of cars and 14 different colors. Determine the number of ways someone can pick a car in a single color.