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Motivation Suppose you want tacos for lunch. The cafeteria has three tortilla choices: corn, flour and hard shell and four meat choices: ground beef,

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Presentation on theme: "Motivation Suppose you want tacos for lunch. The cafeteria has three tortilla choices: corn, flour and hard shell and four meat choices: ground beef,"— Presentation transcript:

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2 Motivation Suppose you want tacos for lunch. The cafeteria has three tortilla choices: corn, flour and hard shell and four meat choices: ground beef, steak, chicken and pork. How many distinct taco combinations are possible?

3 Motivation – Counting Principal Suppose you want tacos for lunch. The cafeteria has three tortilla choices: corn, flour and hard shell and four meat choices: ground beef, steak, chicken and pork. How many distinct taco combinations are possible? Tortilla Choices: Corn (C), Flour (F), Hard Shell (H) Meat Choices: Ground Beef (G), Steak (S), Chicken (Ch), Pork (P)

4 Motivation – Counting Principal Tree Method Tortilla Choices: Corn (C), Flour (F), Hard Shell (H) Meat Choices: Ground Beef (G), Steak (S), Chicken (Ch), Pork (P) FP – Flour with Pork Taco How many choices? Taco Choices CGCGSCSChPFGS PFPHGSChHChP

5 Motivation – Counting Principal Table Method Tortilla Choices: Corn (C), Flour (F), Hard Shell (H) Meat Choices: Ground Beef (G), Steak (S), Chicken (Ch), Pork (P) HG – Hard Shell Taco filled with Ground Beef How many choices? GSChP CCGCSCChCP FFGFSFChFP HHGHSHChHP

6 Motivation – Counting Principal Definitions

7 Fundamental Counting Principal ____________________________________ Tortilla ChoicesMeat ChoicesTotal Choices

8 Fundamental Counting Principal ____________________________________ Tortilla ChoicesMeat ChoicesTotal Choices 3412

9 Examples – Fundamental Counting Principal Suppose you are selecting an outfit to wear to school. You have 5 choices in a top, 4 choices for a bottom and 3 choices in shoes. How many different outfits are possible? How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and the other two digits have no restrictions?

10 Examples – Fundamental Counting Principal Suppose you are selecting an outfit to wear to school. You have 5 choices in a top, 4 choices for a bottom and 3 choices in shoes. How many different outfits are possible? How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and the other two digits have no restrictions? ____________________________ Top Bottom Shoes Total

11 Examples – Fundamental Counting Principal Suppose you are selecting an outfit to wear to school. You have 5 choices in a top, 4 choices for a bottom and 3 choices in shoes. How many different outfits are possible? How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and the other two digits have no restrictions? ____________________________ Top Bottom Shoes Total

12 Examples – Fundamental Counting Principal Suppose you are selecting an outfit to wear to school. You have 5 choices in a top, 4 choices for a bottom and 3 choices in shoes. How many different outfits are possible? How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and the other two digits have no restrictions? ____________________________ Top Bottom Shoes Total ____________________________ First Digit2 nd Digit 3 rd Digit Total

13 Examples – Fundamental Counting Principal Suppose you are selecting an outfit to wear to school. You have 5 choices in a top, 4 choices for a bottom and 3 choices in shoes. How many different outfits are possible? How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and the other two digits have no restrictions? ____________________________ Top Bottom Shoes Total ____________________________ First Digit2 nd Digit 3 rd Digit Total 81010800

14 Examples – FCP Suppose you and your friend are selecting basketball players for a 4-on-4 game. How many distinct teams are possible for this game? Hint: Determine how many players are being selected. How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and no digits repeat?

15 Examples – FCP Suppose you and your friend are selecting basketball players for a 4-on-4 game. How many distinct teams are possible for this game? Hint: Determine how many players are being selected. How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and no digits repeat? ____________________________ 1 st ps2 nd ps3 rd ps4 th ps5 th ps6 th psTotal

16 Examples – FCP Suppose you and your friend are selecting basketball players for a 4-on-4 game. How many distinct teams are possible for this game? Hint: Determine how many players are being selected. How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and no digits repeat? ____________________________ 1 st ps2 nd ps3 rd ps4 th ps5 th ps6 th psTotal 6 5 4 3 2 1 720

17 Examples – FCP Suppose you and your friend are selecting basketball players for a 4-on-4 game. How many distinct teams are possible for this game? Hint: Determine how many players are being selected. How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and no digits repeat? ____________________________ 1 st ps2 nd ps3 rd ps4 th ps5 th ps6 th psTotal ____________________________ First Digit2 nd Digit 3 rd Digit Total 6 5 4 3 2 1 720

18 Examples – FCP Suppose you and your friend are selecting basketball players for a 4-on-4 game. How many distinct teams are possible for this game? Hint: Determine how many players are being selected. How many 3 digit area codes are possible if the first digit cannot be a zero or a 1 and no digits repeat? ____________________________ 1 st ps2 nd ps3 rd ps4 th ps5 th ps6 th psTotal ____________________________ First Digit2 nd Digit 3 rd Digit Total 6 5 4 3 2 1 720 898576

19 Examples – FCP Dependent Events ____________________________ 1 st ps2 nd ps3 rd ps4 th ps5 th ps6 th psTotal 6 5 4 3 2 1 720

20 Classwork Determine the sample space for tossing a fair coin three times. IOW, list all possible outcomes. For the following: determine each event and if the events are independent. An ice cream shop offers a choice of two types of cones and 15 flavors of ice cream. How many different 1-scoop ice cream cones can a customer order? How many different 2-scoop ice cream cones can a customer order if the flavors aren’t repeated? Your history quiz contains 5 true-false questions. How many different choices for giving answers to the 5 questions are possible?

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