Sample Spaces, Tree Diagrams, and the Counting Principle

Jackie is picking out a new skateboard. The board can be dark brown or gray, and the wheels can be orange, green, pink, or yellow. The decal on the skateboard can be a tiger, a diamond, a bear, or an eagle. How many different combinations does Jackie have to choose from?

• 3 combinations

• 8 combinations

• 16 combinations

• 32 combinations

How many styles of sneakers are possible if Jared can choose from high-top or low-top, shoelaces or velcro, and the colors black, white, and red?

• 12

• 7

• 223

• 64

At Papa John's you are deciding on what you want for dinner. The pizza offers 8 different meats, 4 different cheeses, 3 different crust types and 2 different sauces. How many different pizzas do you have to choose from?

• 32

• 192

• 40,320

• 51,200

What is the total number of outcomes for picking a cat or dog and choosing the colors black, brown or spotted?

• 2

• 4

• 6

• 8

Find the total number of outcomes for picking a day of the week and a month of the year.

• 19

• 84

• 60

• 210

Find the total number of outcomes when choosing between plain, BBQ, sour cream & onion, or salt & vinegar potato chips, rippled or regular, in a small or large bag.

• 16

• 24

• 10

• 8

Which of the following situations is represented by this tree diagram?

• 3 shirt options, 6 pants options, and 12 shoe options

• 3 shirt options, 2 pants options, and 2 shoe options

• 2 shirt options, 3 pants options, and 1 shoe option

How many outcomes are there with tossing three quarters?

• 2

• 8

• 12

• 24

Tree Diagram

• A written list of all possible outcomes

• A description of all possible outcomes

• A drawing with branches of all possible outcomes

At a concession stand, you can order a small, medium, or large cola. You can order it with or without ice. How many possible outcomes do you have?

• 3

• 4

• 5

• 6