13-1 Combinations and Permutations

Tree Diagram Independent Event Dependent Event A visual way to show all possible choices Independent Event Events that do not effect each other Examples: Math grade and English Grade Dependent Event Events that do effect each other Semester grades and Final Grade

Section 13.1 Basic Counting Principle (for independent events)– if event 1 can happen x ways, and event 2 can happen y ways, then the probability they happen together is x*y Example) You have three types of shoes and two pants. How many pant/shoe combinations are there?

1) Mrs. Keating needs to choose what to wear to WOHS’s Prom 1) Mrs. Keating needs to choose what to wear to WOHS’s Prom. She has the choice of 3 different dresses, 6 different pairs of shoes, and 10 different hairstyles. She also needs to pick one of 7 different purses and one of 20 different dates. Are these events dependent or independent? How many different selections are available for Mrs. Innerst?

Review: !- factorial 5! = 5 * 4 * 3 * 2 *1 2) What is 6!/3!

Permutations The arrangement of objects in a certain order Order of objects is very important! Example: 3) How many ways can 5 kindergarten kids line up for the bathroom break? 4) You have 5 new songs on your playlist. How many different ways (order) can you listen to them?

What if you don’t use the entire group? If you want to arrange r objects out of n, then P(n,r)= n! (n-r)! n=total r=number you want to arrange 5) How many ways can you arrange only 3 of your 5 books on your shelf.

Is this list independent or dependent? 6) You want to rank your four semester teachers in order from favorite to least favorite. Is this list independent or dependent? How many ways can you list them in different orders?

7) There are 100 kids in the junior class and it is time to vote for class officers. There are positions for President, Vice President, Secretary, and Treasurer. How many ways can these positions be elected? 8) Twenty people are running a race. How many ways can you give our gold, silver, and bronze medals?

Sometimes, instead of a word problem, we’ll just give you n and r in the form P(n,r) Find the following P(5,3) P (7,2)

n=total objects r= number objects you want in each group Combinations The order of selections/events DOES NOT matter. (you’re making “groups”) 𝐶 𝑛,𝑟 = 𝑛! 𝑛−𝑟 ! ∙𝑟! n=total objects r= number objects you want in each group

9) There are 25 kids in Mrs. K’s class and she needs three students to help her run an errand. How many different groups can she create? 10) An art museum has 50 paintings, but only wants to display 5 at a time. How many different group choices are there for the first display?

Difference between Combination and Permutation For Permutation  ORDER MATTERS For Combination ORDER DOES NOT MATTER Think of combining ingredients for cake, order doesn’t matter

11) I want to select five students from the class, with a total of 20 students, to do problems on the board. How many different groups of students can I pick? Does order matter? Is it a combination or permutation? Find the number of groups.

12) The math club has 20 members of which 9 are male and 11 are female 12) The math club has 20 members of which 9 are male and 11 are female. Seven members will be selected to go to a math competition. How many teams of 4 females and 3 males can be formed? How many ways can a president and vice president be chosen for the team?