1 / 14

7.2 Pascal’s Triangle and Combinations

7.2 Pascal’s Triangle and Combinations. 4/10/2013. In today’s lesson we’re learning…. h ow to find the possible number of combinations given a situation and how it relates to Pascal’s triangle. Factorial !. Definition:. The product of an integer and all the integers below it. 0! = 1

chesmu
Download Presentation

7.2 Pascal’s Triangle 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. 7.2 Pascal’s Triangle and Combinations 4/10/2013

  2. In today’s lesson we’re learning… how to find the possible number of combinations given a situation and how it relates to Pascal’s triangle.

  3. Factorial ! Definition: The product of an integer and all the integers below it. 0! = 1 1! = 1 2! = 2•1 =2 3! = 3•2•1 = 6 4!= 4•3•2•1 = 24 How to Calculate:

  4. Combination Definition: is a way of selecting several things out of a larger group, where order does not matter. nCk read as “n Choose k”. That means that you have n number of selections and you’re choosing k amount. nCkis the number of possible combinations from that choice. How it is written:

  5. Example: Ice creamThere are 4 flavors of ice cream you can choose from and you get to pick 2. How many 2-flavor combinations can you have? 4 flavors of ice cream Rocky Road Vanilla Mint Chip Strawberry List of possible combinations: RV RM RS VM VS MS There are 6 combinations. Luckily, there’s a formula you can use instead of making a list!!! Cool huh?

  6. nCkFormula nCk= For the ice cream example: 4C2 “4 choose 2” since there are 4 flavors and you get to choose 2. 4C2 = = 6

  7. Find the number of combinations: nCk= 1. 6C2 6C2 = 2. 7C4 7C4= = 15 = 35

  8. So how does this relate to Pascal’s Triangle? Note: The numbers in the Pascal’s Triangle represents nCk

  9. Now let’s do some word problems! 3 types of problems and what to do. • “exactly” – multiply each group • “at least” – add each group. • “at most” – add each group.

  10. A restaurant gives options of 6 vegetables and 4 meats be ordered in an omelet. Suppose you want exactly 2 vegetables and 3 meats in your omelet. How different omelets can you order? 6C2 for veggies 4C3 for meat “exactly” multiply each group. 6C2•4C3 = 15• 4 = 60 4C3 6C2

  11. You are going to buy a bouquet of flowers. The florist has 18 different types of flowers. You want exactly 3 types of flowers. How many different combinations of flowers can you use in your bouquet? What we have is this: 18C3 Since our Pascal’s Triangle is not big enough to show the 18th row, let’s use the Combination formula. nCk = 18C3= = 816

  12. During the school year, the basketball team is scheduled to play 12 home games. You want to attend at least 9 of the games. How many different combinations of games can you attend? At least 9 games means you can attend 9, 10, 11, 12. So ADD all the possibilities! 12C9 + 12C10 + 12C11 + 12C12 220 + 66 + 12 + 1 = 299

  13. You only like 6 songs on the latest Arcade Fire album. If you want to purchase at most 4 songs with the credit you have on iTunes, how many different combinations can you buy? At most 4 songs means you can buy 0, 1, 2, 3 or 4. So ADD all the possibilities! 6C0 + 6C1+ 6C2+ 6C3+ 6C4 1 + 6 + 15 + 20 +15 = 57

  14. Homework WS 7.2 Skip #s 8, 9, 12 and 14. What does a clock do when it gets hungry??? It goes back four seconds!!!

More Related