1 / 11

15.3 – Permutations and Combinations

15.3 – Permutations and Combinations. 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 :

dena
Download Presentation

15.3 – Permutations and Combinations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 15.3 – Permutations and Combinations Objective: You should be able to solve problems involving permutations and combinations.

  2. 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 1st letter, 2 choices for the 2nd, and 1 choice for the 3rd, there are 3∙2∙1 = 3! = 6 ways to arrange the letters. • In general, the number of permutations of nobjects is n!

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

  4. Permutations of n objects taken r at a time • The number of permutations of r objects taken from a group of n distinct objects is denoted by nPr= Ex. 10P4= =5040

  5. 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?

  6. Combination • a selection of r objects from a group on n objects where the order is NOT important. • Ex. Selecting a governing council of 3 people • nCr= Ex. 10C4= = 210

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

  8. 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?

  9. 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?

  10. 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?

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

More Related