Fundamental Counting Principles

Fundamental Counting Principles

Multiple Choice

Tree Diagram

• A written list of all possible outcomes
• A description of all possible outcomes
• A drawing with branches of all possible outcomes

Multiple Choice

The tree diagram shows the outcomes of rolling a die and flipping a coin.

How many total outcomes are there?

• 6

• 12

• 24

• 36

Multiple Choice

How many total outfit options are represented?

• 12

• 22

• 3

Multiple Choice

Jason can choose 1 pair of pants and one shirt to wear today. Here are his choices. Which tree diagram shows all of the combinations that Jason can choose from?

Multiple Choice

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

Multiple Choice

The cafeteria is serving three kinds of sandwiches: tuna (T), chicken, (C), and peanut butter (P). They are also serving a choice of two drinks: milk (M) or water (W). Which shows the complete set of possible combinations?

• TW, CW, PW

• TW, TM, TC, CW, PW

• TW, TM, CW, CM, PW, PM

• TCP, MW

Multiple Choice

Use the fundamental counting principle to find the total number of outcomes (or outfits) if you have a suitcase with 5 different shirts, 3 types of jackets, 2 different pants, and 3 types of shoes.

• 13, because 5 + 3 + 2 + 3 = 13

• 120, because 5 x 4 x 3 x 2 =120

• 90, because 5 x 3 x 2 x 3 = 90

• 52, because (5 + 3 + 2 + 3) x 4 = 52

Multiple Choice

A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each has a main dish, a salad, and a dessert?

• 5 x 3 x 4 = 60

• 5 + 3 + 4 = 12

Multiple Choice

If Angelo has 12 T – shirts , 6 pairs of pants and 3 pairs of shoes, how many possibilities can he dress himself up for the day ?

• 72

• 16

• 216

• 720

Multiple Choice

If I use the fundamental counting principle, how many different outcomes are there if I flip 4 different 2-sided coins?

• 8, because 4 x 2 = 8

• 6, because 4 + 2 = 6

• 16, because 2 x 2 x 2 x 2 = 16

• 256, because 4 x 4 x 4 x 4 = 256

Multiple Choice

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15

• 40

• 80

• 10

Multiple Choice

A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals could be ordered if each has a main dish, a salad, and a dessert?

• 5 x 3 x 4 = 60

• 5 + 3 + 4 = 12

Multiple Choice

The cafeteria has 2 choices of salads, 3 choices of entrees, and 2 choices of beverages. How many meal combinations are available and why?

• 7 because 2 + 3 + 2

• 12 because 2 x 3 x 2

Multiple Choice

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15

• 40

• 80

• 10