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# 9 3 The Fundamental Counting Principal

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### 9 3 The Fundamental Counting Principal

1. 1. 9-3 The Fundamental Counting Principal Use multiplication to count outcomes A shortcut!!!
2. 2. Turn and Talk <ul><li>Is there a quicker way to find outcomes? </li></ul><ul><li>Rework p 376 </li></ul>
3. 3. Concept Map—Fundamental Counting Principal What, Ex, Compare with tree diagram
4. 4. Find total outcomes <ul><li>Uniform from 3 shirts, 4 pants, 5 colors, and 7 fabrics </li></ul>
5. 5. Find total outcomes <ul><li>4 watches and 4 bands </li></ul>
6. 6. Find total outcomes <ul><li>Buying a car with choices of 6 exterior paint colors, 3 interior colors, and 2 body styles </li></ul>
7. 7. Find total outcomes <ul><li>Class officers: 3 presidential candidates, </li></ul><ul><li>4 vice presidential, 2 secretary, 5 treasurer </li></ul>
8. 8. Find total outcomes <ul><li>Selecting a letter and a 1 digit number </li></ul>
9. 9. Find total outcomes <ul><li>Selecting a vowel and a 1 digit number greater than zero </li></ul>
10. 10. Find total outcomes <ul><li>Tossing a quarter, dime, nickel, and penny </li></ul>
11. 11. Find total outcomes <ul><li>Monogram a bag with initials </li></ul>
12. 12. Find the probability of choosing peanut butter and jelly with orange juice <ul><li>6 different sandwiches and 4 juices </li></ul>
13. 13. Find the probability of picking January and a weekend day <ul><li>Select one month of the year and one day of the week </li></ul>
14. 14. <ul><li>Choose a music system from 4 receivers, 3 speakers, 2 CD players </li></ul><ul><li>Number of outcomes for tossing a coin 5 times </li></ul><ul><li>Number of outcomes for rolling a die twice </li></ul><ul><li>Number of ways to choose a whole number between 1 and 10 and then choose a letter from A through K </li></ul><ul><li>Number of different phone numbers if they cannot begin with 0 </li></ul><ul><li>Number of different phone numbers in Alabama if there are two different area codes and the phone number itself cannot begin with a 0 </li></ul><ul><li>Number of license tags if they begin with 2 digits followed by 3 letters that cannot repeat </li></ul><ul><li>Number of 5 digit zip codes </li></ul>
15. 15. <ul><li>4*3*2=24 outcomes </li></ul><ul><li>2*2*2*2*2=32 outcomes </li></ul><ul><li>6*6=36 outcomes </li></ul><ul><li>8*11=88 outcomes </li></ul><ul><li>9*10*10*10*10*10*10=9,000,000 </li></ul><ul><li>2*9000000=18,000,000 </li></ul><ul><li>10*10*26*25*24=1,560,000 </li></ul><ul><li>10*10*10*10*10=100,000 </li></ul>
16. 16. PIZZA
17. 17. <ul><li>How many different Hoagies can you choose? </li></ul><ul><li>How many different side items can you choose? </li></ul><ul><li>How many choices of pizza toppings are there? </li></ul><ul><li>How many specialty pizzas does Buck have? </li></ul><ul><li>How many ways can you choose a hoagie and a side item? </li></ul><ul><li>How many different ways can you choose one of the specialty pizzas and a side item? </li></ul><ul><li>How many different ways can you order a small pizza with one topping and a medium pizza with one topping? </li></ul><ul><li>How many ways can you order a large pizza with one topping and a hoagie? </li></ul>
18. 18. <ul><li>6 hoagies </li></ul><ul><li>7 side items </li></ul><ul><li>16 toppings </li></ul><ul><li>11 pizzas </li></ul><ul><li>42 ways </li></ul><ul><li>77 ways </li></ul><ul><li>256 ways </li></ul><ul><li>96 ways </li></ul>Answers:
19. 19. Venn Diagram <ul><li>Tree Diagram and fundamental counting principal </li></ul>
20. 20. Homework <ul><li>P 379: 1-22 </li></ul>