9-3 The Fundamental Counting Principal

Use multiplication to count outcomes

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Concept Map—Fundamental Counting PrincipalWhat, Ex, Compare with tree diagram

Find total outcomes

• Uniform from 3 shirts, 4 pants, 5 colors, and 7 fabrics

Find total outcomes

• 4 watches and 4 bands

Find total outcomes

• Buying a car with choices of 6 exterior paint colors, 3 interior colors, and 2 body styles

Find total outcomes

• Class officers: 3 presidential candidates,

4 vice presidential, 2 secretary, 5 treasurer

Find total outcomes

• Selecting a letter and a 1 digit number

Find total outcomes

• Selecting a vowel and a 1 digit number greater than zero

Find total outcomes

• Tossing a quarter, dime, nickel, and penny

Find total outcomes

• Monogram a bag with initials

Find the probability of choosing peanut butter and jelly with orange juice

• 6 different sandwiches and 4 juices

Find the probability of picking January and a weekend day

• Select one month of the year and one day of the week

1) Choose a music system from 4 receivers, 3 speakers, 2 CD players

2) Number of outcomes for tossing a coin 5 times

3) Number of outcomes for rolling a die twice

4) Number of ways to choose a whole number between 1 and 10 and then choose a letter from A through K

5) Number of different phone numbers if they cannot begin with 0

6) Number of different phone numbers in Alabama if there are two different area codes and the phone number itself cannot begin with a 0

7) Number of license tags if they begin with 2 digits followed by 3 letters that cannot repeat

8) Number of 5 digit zip codes

1) 4*3*2=24 outcomes

2) 2*2*2*2*2=32 outcomes

3) 6*6=36 outcomes

4) 8*11=88 outcomes

5) 9*10*10*10*10*10*10=9,000,000

6) 2*9000000=18,000,000

7) 10*10*26*25*24=1,560,000

8) 10*10*10*10*10=100,000

1. How many different Hoagies can you choose?2. How many different side items can you choose?3. How many choices of pizza toppings are there?4. How many specialty pizzas does Buck have?5. How many ways can you choose a hoagie and

a side item?6. How many different ways can you choose one

of the specialty pizzas and a side item?7. How many different ways can you order a small

pizza with one topping and a medium pizza with one topping?

8. How many ways can you order a large pizza with one topping and a hoagie?

1. 6 hoagies

2. 7 side items

3. 16 toppings

4. 11 pizzas

5. 42 ways

6. 77 ways

7. 256 ways

8. 96 ways

Venn Diagram

• Tree Diagram and fundamental counting principal

Homework

• P 379: 1-22