1. Wednesday by Dave And Brian
Wednesday by Dave And Brian

2. Sixteen runners are racing
Sixteen runners are racing. In how many ways can 1st, 2nd, and 3rd place prizes be awarded?

6. Math 1 section 11-1: permutations and combinations
section 11-2: theoretical and experimental probability

7. Fundamental Counting Principle
chapter 11 – probability and statistics
Fundamental Counting Principle
If there are n items and m1 ways to pick the first item,
m2 ways to pick the second item
m3 ways to pick the third item
m4 ways to pick the fourth item and so forth,
Then there are m1lm2 lm3 lm4l…lmn ways to choose the n items.

8. example 1: using the fundamental counting principle
chapter 11 – probability and statistics
example 1: using the fundamental counting principle
To make a yogurt parfait, you choose one flavor of yogurt, one fruit topping, and one nut topping. How many parfait choices are there? A
Yogurt Parfait
(choose 1 of each)
(Flavor)
Plain
Vanilla
(Fruit)
Peaches
Strawberries
Bananas
Raspberries
Blueberries
(Nuts)
Almonds
Peanuts
Walnuts
There are 30 different parfait choices.
A local burrito restaurant offers 4 types of meat and 2 types of beans. If you pick one of each, how many different burritos can you make? B
You can make 8 different burritos.

9. The selection of a group of objects in which order is important.
chapter 11 – probability and statistics
Permutation
The selection of a group of objects in which order is important.
In how many ways can 5 students be arranged in a line? 5 4 3 2 1
_____ , _____ , _____ , _____ , _____
Ask yourself this question, how many choices for the first person?
How many choices for the second person?
How many choices for the third person?
The counting principle says to multiply the choices.
There are 120 different ways to arrange the students.

10. n Factorial 3,628,800 different ways
chapter 11 – probability and statistics
In how many ways can 10 students be arranged in a line?
___ ___ ___ ___ ___ ___ ___ ___ ___ ___
Ask yourself this question, how many choices for each person?
There is a function and special symbol for this calculation.
n Factorial
The factorial of a number, n , is the product of the natural numbers less than or equal to that number.
The symbol is n!
There are 10! different ways to arrange the students.
3,628,800 different ways

11. chapter 11 – probability and statistics
Simplify the following.

12. chapter 11 – probability and statistics
Suppose you have 7 books and want to arrange 3 of them on a shelf. 7 6 5
= 210
_____ , _____ , _____
Another way to think about this situation is
210

13. The selection of a group of objects in which order does not matter.
chapter 11 – probability and statistics
Combination
The selection of a group of objects in which order does not matter.
Take the permutations of the letters A, B, C. There are 6 (3.2.1)
ABC, ACB, BAC, BCA, CAB, CBA
Since in a combination, order does not matter, these are the same.
Divide the permutation by the # of ways to arrange the selected items.

14. example 2: finding permutations/combinations
chapter 11 – probability and statistics
example 2: finding permutations/combinations
George has 5 friends named Samuel, Joe, Albert, Bill, and Lebron.
How many ways can he select a President, Vice President, and a secretary from this group of 5 people? A
George is going on a road trip and needs to pick three friends to take with him. How many ways can he pick 3 people from this group of 5? B

15. example 2: finding permutations/combinations
chapter 11 – probability and statistics
example 2: finding permutations/combinations C D

16. example 1: permutations/combinations
chapter 11 – probability and statistics
example 1: permutations/combinations A
How many ways can a club select a president, secretary, and a treasurer from a group of 8 people?
8P3 = 336 B
An art gallery has 9 paintings from an artist and will display 4 from left to right on a wall. In how many ways can the gallery display the paintings?
9P4 = 3024 C
How many ways can a committee of 5 be selected from a group of 12 people?
12C5 = 792
The swim team has 8 swimmers. 3 will be selected to swim the first heat. How many ways can the swimmers be picked? D
8C3 = 56

17. theoretical and experimental probability
chapter 11 – probability and statistics
theoretical and experimental probability
example 3: finding theoretical probability

18. chapter 11 – probability and statistics
example 1: probability A
What is the probability of rolling a 5 with a standard die? B
What is the probability of not rolling a 5 with a standard die?
The complement of an event E is the set of all outcomes in the sample space that are not in E. C
If the probability of passing a test is .82, what is the probability of not passing the test?
If the probability running out of gas is , what is the probability of not running out of gas? D

19. example 3: finding probability using permutations/combinations
chapter 11 – probability and statistics
example 3: finding probability using permutations/combinations
An Algebra class has 5 ninth-graders, 17 sophomores, and 3 eighth-graders.
If you select one student at random, what is the probability that you will select an 8th grader? A

20. example 4: finding geometric probability
chapter 11 – probability and statistics
example 4: finding geometric probability
What is the probability of landing on light blue?
What is the probability of landing on pink?
What is the probability of not landing on black?

21. chapter 11 – probability and statistics