Name: ______Date: ______

Math 7AC

Do Now: Andy has 5 shirts, 3 pairs of pants, and 6 pairs of socks. How many different outfits can Andy choose with a shirt, a pair of pants, and a pair of socks?

Draw a tree diagram to show the possible outcomes

Fundamental Counting Principle

.

number of shirts × number of pants × number of socks = total number of outfits

______× ______× ______= ______

Therefore, Andy can choose ______different outfits.

Example 2: Find the total number of outcomes when a coin is tossed and a number cube is rolled.

# of outcomes on a coin × # of outcomes on a cube = total # of outcomes

______× ______= ______

Therefore, there are ______different outcomes.

Now, Let's try these:

For #'s 1 - 6, use the Fundamental Counting Principle to find the total number of outcomes in each situation.

1. choosing one of 3 processor speeds, 2 sizes of memory, and 4 sizes of hard drive

2. choosing a 4-, 6-, or 8-cylinder engine and 2- or 4-wheel drive

3. rolling two number cubes

4. tossing 3 coins

5. choosing a color from 4 colors and a whole number from 4 to 10

6. picking a month of the year and a day of the week

7. The Jeans Shop sells young men's jeans in different sizes, styles, and lengths according to the table below.

Waist Size / Length / Style
30 / 30 / Slim fit
32 / 32 / Bootcut
34 / 34 / Loose fit
36
38

a) Find the number of jeans available.

b) Find the probability of randomly selecting a size 32 waist, 34 length, slim fit. Express your answer as a fraction

anda percent. Is this likely or unlikely that this size will be chosen?

8. The table shows thekinds of homes offered by a residential builder.

Number of Bedrooms / Style of Kitchen / Type of Porch
5-bedroom / Mediterranean / Open
4-bedroom / Contemporary / Screen
3-bedroom / Southwestern

a)Find the total number of homes available.

b) If the builder offers a discount on one home at random, find the probability it will be a 4-bedroomhome with an

open porch. Explain your reasoning.

Name: ______Date: ______

Math 7AC

Homework: Fundamental Counting Principle

For #'s 1 - 10, use the Fundamental Counting Principle to find the total number of outcomes in each situation.

1. choosing from 8 car models, 5 exterior paint colors, and 2 interior colors

2. picking from 3 theme parks and 1-day, 2-day, 3-day, and 5-day passes

3. choosing a meat and cheese sandwichfrom the list shown in the table

Cheese / Meat
Provolone / Salami
Swiss / Turkey
American / Tuna
Cheddar / Ham

4. tossing a coin and rolling 3 number cubes

5. selecting coffee in regular or decaf, with or withoutcream, and with or without sweeteners

6. choosing from 35 flavors of ice cream; one, two, or three scoops; and sugar or waffle cone

7. rolling 3 number cubes and 2 coins

8. choosing a bicycle with or without shock absorbers; with or without lights; and 5 colors

9. choosing from 3 sizes of bottled water and from distilled, filtered, or spring water

10. picking an odd number from 3 to 11 and choosing from 5 colors

11. A store advertises that they have a different T-shirt for each day of the year. The store offers 32 different t-shirt designs and 11 choices of color. Is the advertisement true? Explain.

12. Mira has 3 sweaters, 4 blouses and 6 skirts that coordinate.

a) Find the number of different outfits consisting of a sweater, blouse, and skirt that are possible.

b) Find the probability of randomly selecting a particular sweater-blouse-skirt outfit. State the probability as a

fraction and as a percent. Is the probability of this event likely or unlikely?

13. Which one doesn't belong? Identify the choices for events M and N that do not result in the same number of outcomes as the other two. Explain your reasoning.