# Lesson Worksheet: Representing Sample Spaces Mathematics

In this worksheet, we will practice using tables and tree diagrams to represent a sample space and using the fundamental counting principle to find possible outcomes.

**Q1: **

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?

**Q2: **

Suppose 4 fair coins are tossed at the same time that these two spinners are spun. Using the fundamental counting principle, find the total number of possible outcomes.

**Q3: **

Use the fundamental counting principle to find the total number of outcomes of rolling 4 number cubes and tossing 2 coins.

**Q4: **

In a small town, there are 4 paths connecting the library and the post office, 5 paths connecting the post office and the bank, and 2 paths connecting the bank and the park. Determine the number of ways to walk from the library to the park.

**Q5: **

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?

**Q6: **

Use the fundamental counting principle to determine the total number of outcomes of picking out an outfit from 4 shirts, 8 pairs of pants, and 2 jackets.

**Q7: **

Suppose there are 9 sheep whose fur may be only one of two colors, white or brown. Using the tree diagram, determine the total number of possible sheep-color choices.

**Q8: **

A restaurant offers a set menu with four choices of appetizers, five choices for the main course, and three choices for dessert. Assuming somebody orders all three courses, how many different possible meals can they choose?

**Q9: **

Joud goes away for the weekend. She takes with her five jumpers, three skirts, and two pairs of shoes. How many different outfits can she wear?

**Q10: **

Alanoud wants to purchase a new car. There are 6 different options for the color, 4 different options for the interior, 5 different options for the engine size, and 2 different options for the fuel type. How many different options does Alanoud have overall for her new car?