1. C OUNTING T ECHNIQUES, P ERMUTATIONS, AND C OMBINATIONS Created by Charell Wingfield

2. THINK- PAIR- SHARE Ms. Wingfield just loves her shoes. Today, however, she is having a crisis. She cannot find anything to wear. She has 2 pairs of shoes, 4 skirts, and 3 blouses. How many different outfits could she make? 24 Outfits

3. TREE DIAGRAM

4. COUNTING TECHNIQUES Based on independent events Tree diagram method The Fundamental Counting Principle also known as the Multiplication RuleFundamental Counting Principle

5. FUNDAMENTAL COUNTING PRINCIPLE If an even M occurs in m ways and is followed by an event N that can occur in n ways, then the event M followed by event N can occur in m * n ways.

6. E XAMPLE · Suppose Panera Bread has a $6.99 dinner option where you get to pick a soup, a sandwich, and a milk shake. You have 2 choices for soup: Broccoli and Cheddar Soup and Baked Potato Soup You have 3 choices for sandwiches: Bacon Turkey Bravo, Chicken Cesear, and BLT You have 3 choices for milk shakes: Vanilla, Chocolate, and Strawberry If you are allowed to pick one soup, one sandwich, and one milk shake, how many different dinner combinations are there? ___________ (An example of a dinner combination is Potato Soup, BLT, and a Vanilla milk shake.)

7. P ERMUTATIONS Another name for possible arrangements with SOME items from a given set. Order matters Examples: Creating a telephone number, selecting the winners of a race, generating a social security number Mathematical Formula

8. Example How can we arrange a set of 5 numbers out of 9 to create a zip code? 9 P 5 = 9! = 9! (9-5)! 4!

9. COMBINATIONS An arrangements of elements without regard to their order or position. Order does NOT matter Examples: Selecting the toppings for a sandwich or choosing 5 cards from a deck Mathematical Formula

10. EXAMPLE Pick which three meats among Roast Beef (R), Ham (H), Turkey (T), Pepperoni (P), and Salami (S) to put on your sandwich. It does not really matter which order you put the meats on your sandwich. How many ways can we do this? (RHT, RHP, RHS, RTP, RTS, RPS, HTP, HTS, HPS, TPS) 10 ways!

11. TI-Nspire Instructions Press the Home button. Go to 1:Calculator. Press Menu >> 5: Probability For Permutations, press 2: Permutations For Combinations, press 3: Combinations **When entering the numbers for permutations and combinations, separate the n an r terms with a comma.

12. CLASS WORK

13. WHAT’S THE DIFFERENCE??? Selection of objects from a group Order Matters Selection of objects from a group Order is not important PERMUTATIONCOMBINATION

14. Homework Assignment *Create an organizational chart of some form in which you compare and contrast the similarities and differences between counting techniques, permutations, and combinations. You may demonstrate your understanding in the form of a venn diagram, organizational chart, flow chart, etc. *Also, create your own original examples of when the Fundamental Counting Principle, permutations, and combinations will be used.

15. Counting Techniques CombinationsPermutations

16. Likelihoods of Occurrence Counting Techniques PermutationsCombinations

17. Determining the Outcomes Counting Techniques CombinationsPermutations