1. Algebra 1 Notes: Probability Part 2: Counting Outcomes

2. Objectives Calculate the number of possible outcomes using the fundamental counting principle

3. Take A Guess How many different ways can I line up 8 students for a picture?

4. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

5. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

6. Example 1 Bread

7. Example 1 Bread wheat rye

8. Example 1 BreadMeat wheat rye

9. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

10. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

11. Example 1 BreadMeat salami wheat turkey ham rye

12. Example 1 BreadMeat salami wheat turkey ham salami ryeturkey ham

13. Example 1 BreadMeatSide Item salami wheat turkey ham salami ryeturkey ham

14. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

15. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

16. Example 1 BreadMeatSide Item chips salamibrownie fruit wheatturkey ham salami ryeturkey ham

17. Example 1 BreadMeatSide ItemOutcomes chips 1 salamibrownie 2 fruit 3 wheatturkey ham salami ryeturkey ham

18. Fundamental Counting Principle Multiply the number of ways EACH event can occur.

19. Example 1 At football games, a student concession stand sells sandwiches on either wheat or rye bread. The sandwiches come with salami, turkey or ham; and either chips, a brownie, or fruit. Use a tree diagram to determine the number of possible sandwich combinations.

20. BreadsMeatSideTotal 2x 3 x 3 =

21. BreadsMeatSideTotal 2x 3 x 3 = 18

22. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drive choices 11

23. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboard choices choices 11

24. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboard choices choices 11 6

25. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmouse choices choiceschoices 11 6

26. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmouse choices choiceschoices 11 6 4

27. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4

28. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4

29. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4

30. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4 = 1,056

31. Example 2 The Too Cheap computer company sells custom made personal computers. Customers have a choice of 11 different hard drives, 6 different keyboards, 4 different mice, and 4 different monitors. How many different custom computers can you order? hard drivekeyboardmousemonitor choices choiceschoiceschoices 11 6 4 4 = 1,056 different computers

32. Vocabulary Factorial – A number multiplied by every positive integer less than itself Looks like an exclamation point.

33. Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture?

34. Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture? 8 7 6 5 4 3 2 1

35. Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture? 8 7 6 5 4 3 2 1 = 8!

36. Example 3 There are 8 students in the Biology Club at Central High School. The students want to stand in line for their yearbook picture. How many different ways could the 8 students stand for their picture? 8 7 6 5 4 3 2 1 = 8! = 40,320 40,320 ways they could stand

37. Homework Worksheet: Counting Outcomes