1. The Fundamental Counting Principle 10-6 Learn to find the number of possible outcomes in an experiment.

2. The Fundamental Counting Principle 10-6

3. The Fundamental Counting Principle 10-6 License plates are being produced that have a single letter followed by three digits. All license plates are equally likely. Example 1A: Using the Fundamental Counting Principle Find the number of possible license plates. Use the Fundamental Counting Principal. letterfirst digit second digit third digit 26 choices10 choices 26 10 10 10 = 26,000 The number of possible 1-letter, 3-digit license plates is 26,000.

4. The Fundamental Counting Principle 10-6 Example 1B: Using the Fundamental Counting Principal Find the probability that a license plate has the letter Q. 1 10 10 10 26,000 = 1 26  0.038 P(Q ) =

5. The Fundamental Counting Principle 10-6 Example 1C: Using the Fundamental Counting Principle Find the probability that a license plate does not contain a 3. First use the Fundamental Counting Principle to find the number of license plates that do not contain a 3. 26 9 9 9 = 18,954 possible license plates without a 3 There are 9 choices for any digit except 3. P(no 3) = = 0.729 26,000 18,954

6. The Fundamental Counting Principle 10-6 Social Security numbers contain 9 digits. All social security numbers are equally likely. Example 2A Find the number of possible Social Security numbers. Use the Fundamental Counting Principle. Digit123456789 Choices10 10 10 10 10 10 10 10 10 10 = 1,000,000,000 The number of Social Security numbers is 1,000,000,000.

7. The Fundamental Counting Principle 10-6 Example 2B Find the probability that the Social Security number contains a 7. P(7 _ _ _ _ _ _ _ _) = 1 10 10 10 10 10 10 10 10 1,000,000,000 = = 0.1 10 1

8. The Fundamental Counting Principle 10-6 Example 2C Find the probability that a Social Security number does not contain a 7. First use the Fundamental Counting Principle to find the number of Social Security numbers that do not contain a 7. P(no 7 _ _ _ _ _ _ _ _) = 9 9 9 9 9 9 9 9 9 1,000,000,000 P(no 7) = ≈ 0.4 1,000,000,000 387,420,489

9. The Fundamental Counting Principle 10-6 The Fundamental Counting Principle tells you only the number of outcomes in some experiments, not what the outcomes are. A tree diagram is a way to show all of the possible outcomes.

10. The Fundamental Counting Principle 10-6 Example 3: Using a Tree Diagram You have a photo that you want to mat and frame. You can choose from a blue, purple, red, or green mat and a metal or wood frame. Describe all of the ways you could frame this photo with one mat and one frame. You can find all of the possible outcomes by making a tree diagram. There should be 4 2 = 8 different ways to frame the photo.

11. The Fundamental Counting Principle 10-6 Example 3 Continued Each “branch” of the tree diagram represents a different way to frame the photo. The ways shown in the branches could be written as (blue, metal), (blue, wood), (purple, metal), (purple, wood), (red, metal), (red, wood), (green, metal), and (green, wood).

12. The Fundamental Counting Principle 10-6 Example 4 A baker can make yellow or white cakes with a choice of chocolate, strawberry, or vanilla icing. Describe all of the possible combinations of cakes. You can find all of the possible outcomes by making a tree diagram. There should be 2 3 = 6 different cakes available.

13. The Fundamental Counting Principle 10-6 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

14. The Fundamental Counting Principle 10-6 Lesson Quiz: Part I Personal identification numbers (PINs) contain 2 letters followed by 4 digits. Assume that all codes are equally likely. 1. Find the number of possible PINs. 2. Find the probability that a PIN does not contain a 6. 0.6561 6,760,000

15. The Fundamental Counting Principle 10-6 Lesson Quiz: Part II A lunch menu consists of 3 types of sandwiches, 2 types of soup, and 3 types of fruit. 3. What is the total number of lunch items on the t menu? 4. A student wants to order one sandwich, one t bowl of soup, and one piece of fruit. How many t different lunches are possible? 18 8

16. The Fundamental Counting Principle 10-6 1. A login password contains 3 letters followed by 2 digits. Identify the number of possible login passwords. A. 175,760 B. 676,000 C. 1,757,600 D. 6,760,000 Lesson Quiz for Student Response Systems

17. The Fundamental Counting Principle 10-6 2. Employee identification codes at a company contain 2 letters followed by 4 digits. Assume that all codes are equally likely. Identify the probability that an ID code does not contain the letter I. A. 0.6567 B. 0.7493 C. 0.8321 D. 0.9246 Lesson Quiz for Student Response Systems

18. The Fundamental Counting Principle 10-6 3. A restaurant offers 4 main courses, 3 desserts, and 5 types of juices. What is the total number of items on the menu? A. 3 B. 7 C. 9 D. 12 Lesson Quiz for Student Response Systems

19. The Fundamental Counting Principle 10-6 4. A restaurant offers 3 types of starters, 4 types of sandwiches, and 4 types of salads for dinner. Visitors select one starter, one sandwich, and one salad. How many different dinners are possible? A. 3 B. 4 C. 11 D. 48 Lesson Quiz for Student Response Systems