1. Fundamental Counting Principle
Lesson 9-5

2. Fundamental Counting Principle
If event M has m possible outcomes and even N has n possible outcomes, then event M followed by event N has m x n possible outcomes. You can use multiplication instead of making a tree diagram to find the number of possible outcomes in a sample space. This is called the Fundamental Counting Principle.

3. Example 1
Find the total number of outcomes when a coin is tossed and a number cube is rolled. A coin has 2 possible outcomes and a die has 6 possible outcomes. Multiple the possible outcomes together. There are 42 possible outcomes.

4. Got it? 1
Find the total number of outcomes when choosing from bike helmets that come in three colors and two styles. Draw a tree diagram if needed.

5. Example 2
You can use the Fundamental Counting Principle to help find the probability of events.
Find the total number of outcomes from rolling a die and choosing a letter in the word NUMBERS. Then find the probability of rolling a 6 and choosing an M.
There are 42 different outcomes. So the probability is or about 2%

6. Example 3
Find the number of different jeans available at The Jean Shop. Then find the probability of randomly selecting a size 32 x 24 slim fit. Is it likely or unlikely that the jeans would be chosen? There are 45 different types, so there’s a 1 45 or about 2%.

7. Got it? 2 & 3
Two dice are rolled. What is the probability that the sum of the numbers on the cube is 12? How likely is it that the sum would be 12?

8. Example 4
A box of toy cars contains blue, orange, yellow, red, and black cars. A separate box contains a math and female action figure. What is the probability of randomly choosing an orange car and a female action figure? Is it likely or unlikely that this combination is chosen? There are 5 choices and 2 genders. 5 x 2 = 10 Probability = 1 10 or 10% P(orange, female) is very unlikely.

9. Got it? 4
Two spinners are spun. What is the probability that the product of two numbers that is spun is 12? How likely is that the product would be 12?

10. Lesson Homework
C = #1 – 4, 6 – 7, 11, 12
A = #5, 8, 9

11. Permutations
Lesson 9-6

12. Permutations 1. An arrangement, or listing, of objects
2. Order matters
Example: Blue, Red, Green ≠ Red, Green, Blue
Use the Probability Multiplication Rule to find the number of permutations.

13. Example 1
Julia is scheduling her first three classes. Her choices are math, science, and language arts. Find the number of different ways Julia can schedule her first three classes.

14. Example 2
An ice cream shop has 31 flavors. Carlos wants to buy a three-scoop cone with three different flavors. How many cones could he buy if the order of flavors are important? 31 • 30 • 29 = 26,970 He could buy 26,970 different ice cream cones.

15. Got it? 1 & 2
a. In how many ways can the starting six players of a volleyball team stand in a row for a picture?
b. In a race with 7 runners, in how many ways can the runners end up in first, second, and third?

16. Permutations
The symbol P(31,3) represents the number of permutations of 31 things taken 3 at a time.

17. Example 3
Find P(8, 3). P(8, 3) = 8 • 7 • 6 = 336

18. Got it? 3
Find P(12, 2)
Find P(4, 4)
Find P(10, 5)

19. Example 4
Ashley’s iPod has a setting that allows the songs to play in a random order She has a playlist that contains 10 songs. What is the probability that the iPod will randomly play the first three songs in order. Find P(10, 3). P(10, 3) = 10 • 9 • 8 = 720 So the probability is

20. Example 5
A swimming event features 8 swimmers. If each swimmer has an equally likely chance of finishing in the top two, what I the probability that Yumli will be in first place and Paquita is in second place? Find the permutation of 8 things taken two at a time. P(8, 2) = 8 • 7 = 56 The probability is

21. Got it? 4 & 5
Two different letters are randomly selected from the letters in the word MATH. What is the probability that the first letter selected is “M” and the second letter is “H”?

22. Lesson Homework
C = #1 – 7, 10, 13
A = #8, 9, 11 or 12

23. Independent and Dependent Events
Lesson 9-7

24. Independent Events is when one event does not affect another event.

25. We will continue to use tree diagrams to show sample space.
Key Concept:
We will continue to use tree diagrams to show sample space.

26. There are 12 outcomes. Two only contains only vowels.
Example 1
One letter tile is selected and the spinner is spun. What is the probability that both will be a vowel?
Make a tree diagram
There are 12 outcomes. Two only contains only vowels.
2 12 = 1 6

27. P(selecting a vowel) = 2 4 𝑜𝑟 1 2
Example 1
One letter tile is selected and the spinner is spun. What is the probability that both will be a vowel?
Use Multiplication
P(selecting a vowel) = 𝑜𝑟 1 2
P(spinning a vowel) = 1 3
P(both vowels) = • 1 3 = 1 6

28. Example 2
The spinner and dice shown are used in a game. What is the probability of a player not spinning a blue and then rolling a 3 or 4? P(not blue) = 4 5 P(3 or 4) = 2 6 or 1 3 P(not blue and 3 or 4) = 4 5 • 1 3 = 4 15

29. Got it? 2
A game requires players to roll two dice to move their game piece. The faces of the cube are labeled 1 through 6. What is the probability of rolling a 2 or 4 on the first number and then rolling a five on the second one?

30. Probability of Dependent Events
If the outcome of one event affects another event, the events are dependent.

31. Example 3
There are 4 oranges, 7 bananas, and 5 apples in a fruit basket. Ignacio selects a piece of fruit at random. Find the probability that two apples are chosen. P(first is an apple) = 5 16 P(second is an apple = 4 15 P(both are apples) = 5 16 • 4 15 = or 1 12 The probability is

32. Got it?
There are 4 oranges, 7 bananas, and 5 apples in a fruit basket.
a. Find P(two bananas)
b. Find P(orange then apple)

33. Lesson Homework
C = #1 – 10, 13
A = #11, 12, 15