Wednesday by Dave And Brian http://www.youtube.com/watch?v=UKZfDLxVIkU Wednesday by Dave And Brian

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

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

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.

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.

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.

n Factorial 3,628,800 different ways chapter 11 – probability and statistics In how many ways can 10 students be arranged in a line? ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 10 9 8 7 6 5 4 3 2 1 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

chapter 11 – probability and statistics Simplify the following.

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

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.

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

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

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

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

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 .000375, what is the probability of not running out of gas? D

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

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?

chapter 11 – probability and statistics