Objective: You should be able to solve problems involving permutations and combinations.

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Presentation transcript:

Objective: You should be able to solve problems involving permutations and combinations.

Permutation Order of selection IS important. Ex. Selecting President, Vice President, and Treasurer ***There are 6 permutations of the letters A, B, and C: ABC, ACB, BCA, BAC, CAB, and CBA. Since there are 3 choices for the 1 st letter, 2 choices for the 2 nd, and 1 choice for the 3 rd, there are 3∙2∙1 = 3! = 6 ways to arrange the letters. In general, the number of permutations of n objects is n!

Example: You have homework assignments from 5 different classes to complete this weekend. In how many different ways can you complete the assignments?

Permutations of n objects taken r at a time

Example: The Bulls have two starting positions open, a point guard and a small forward. If 15 people who are qualified for either position try out, in how many ways can the opening be filled?

Combination

Example: The Celtics have two non-starting forward positions available. In how many ways can the positions be filled if 22 people try out?

Example: For a certain raffle, 845 tickets are sold. a. In how many ways can four $50 gifts cards be awarded? b. In how many ways can a $100, a $50, a $20, and a $10 gift card be awarded?

Example: At the Denny’s, an omelet can be ordered plain or with any or all of the following fillings: cheese, onions, peppers. How many different kinds of omelets are possible?

Example: a) You are taking a vacation and can visit as many as 5 different cities and 7 different attractions. Suppose you want to visit exactly 3 different cities and 4 different attractions. How many different trips are possible?

Example cont. b) Suppose you want to visit at least 8 locations (cities or attractions). How many different types of trips are possible?