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### Pre-Algebra

Fundamental Counting Principle

What Are You Learning?

- I CAN use the fundamental counting principle to find the total number of outcomes.

Why Do You Need To Know This?

- The fundamental counting principle is useful because it give another way to find the sample space of various real world events.
- They are also useful in finding the probabilities of various events.

Vocabulary

- Fundamental Counting Principle—If an event M can occur in m ways and is followed by event N that can occur in n ways, then the event M followed by N can occur in m x n ways.
- You multiply the number of ways each event can happen.

451 Steakhouse

- A famous steak house allows customers to create their own steak dinners.
- How many different steak dinners are possible?

The table below shows the shirts, shorts, and shoes in Gerry’s wardrobe.

- How many possible outfits can he choose consisting of one shirt, one pair of shorts, and one pair of shoes?

An orchestra has one opening for a violinist, one opening for a cellist, and one opening for an oboist. 3 musicians are trying out for violin, 5 for cello, and 3 for oboe.

- Find the # of ways the openings can be filled.

There are 2 roads connecting Eastland and Harping, 3 roads connecting Harping and Sinclair, and 2 roads connecting Sinclair and Johnstown.

- Find the number of ways to drive from Eastland to Johnstown.

Elizabeth has 3 sweaters, 5 blouses, and 6 skirts that coordinate.

- How many different outfits can Elizabeth make?

tossing a quarter, dime, and a nickel

choosing scrambled, sunny-side up, or poached eggs with bacon or sausage and milk, orange juice, or apple juice

rolling a number cube and tossing two coins

choosing a number from 1 to 20 and a color from 7 colors

choosing a plain, blueberry, garlic, or cinnamon-and-raisin bagel with plain, chive, or sun-dried tomato cream cheese

choosing iced tea in regular, raspberry, lemon, or peach flavors; sweetened or unsweetened; and in a glass or in a plastic container

Use the Fundamental Counting Principle to find the total number of outcomes for each situation.
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