BELLWORK UNIT 6 PROBABILITY At an amusement park, you want to go Splash Down on all of the rides Lo op shown on the Ti de ltin Lo g op T signpost. In how ow er s many different orders can you go Ferris Wheel on the rides? Describe how you found the answer. Permutations and Combinations SPI 5.5: Determine theoretical and/or experimental probability of an event and/or its complement including relative frequency Agenda Tree Diagram Fundamental Counting Principle Factorial Permutations nPr Combinations nCr Practice and Apply Bellwork Agenda Tree Diagrams Can be used to show possible outcomes Watching 3 movies:Comedy, Drama, Action Drama Action Action Drama Comedy Action Action Comedy Comedy Drama Comedy Drama Action Drama Fundamental Counting Principle Another way to find the total possible outcomes without drawing a tree diagram Multiply the number of choices for each instance How many different sandwiches can be made with 3 choices of bread, 4 meats, and 2 cheeses? Choices for bread Choices for meats Choices for cheeses Total Possible Outcomes Comedy Tree Diagram Counting Principle Try the Counting Principle for the Movie Example Factorial n! 5! = Try the Counting Principle to find the total Possible combinations if a pizza shop offers 8 vegetables toppings and 6 meat toppings 10! = Try... 3! 6! 12! Counting Principle Try Factorial 1 Permutations: an arrangement of objects in a specific order (order matters) PERMUTATIONS 7 P5 1st, 2nd, 3rd place in a race 10 P3 A committee A relay race 17 P4 Permutations TRY 3 P2 PERMUTATIONS 7 P4 Permutations Ex TRY 11 P5 Combinations: an arrangement of objects without regard to order (order does not matters) three scoops of ice cream Group for group work Four newspaper articles Permutations Try COMBINATIONS Combinations TRY 5 8 C2 COMBINATIONS 8 C3 TRY 15 C7 C4 11 C5 18 C3 Combinations Ex Combinations Try 2 Practice and Apply P.754 #1524, 2736, 4045, 5661 SPI 5.5 Permutations and Combinations Practice and Apply 3
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