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Lesson 1: Combinations and Permutations
Step 1: Probabilities of Outcomes Overview
You can begin the lesson by reviewing the multiplication principle when determining the outcomes of multiple events.
Multiplication rule: if one event can occur in b different ways and another event can occur in s different ways, then the number of different ways the two events combined can occur is b x s.
Question 1: Josh is getting dressed. For pants, he can choose either his black pants or jeans, and for shirts he has one white, one blue and one black. How many different outfits can he choose? Ask students to draw a tree diagram and use it to count the possibilities. Show the possibilities in a grid? Now form an equation using the multiplication principle (event b represents Josh's pant choice, event s represents Josh's shirt choice)
Answers:
a tree diagram:
a grid:
| WS | RS | BS | |
| BP | BP / WS | BP / RS | BP / BS |
| J | J / WS | J / RS | J / BS |
An equation: b x s = 2 x 3 = 6
Question 2: Emily is ordering her lunch at the cafeteria. For an appetizer she can choose either a salad or soup. For the main course she can choose macaroni and cheese, chicken casserole, lasagna or fishcakes, and for dessert she can choose ice cream, chocolate cake or blueberry pie. How many different lunch combinations could she have?
Answer: 2 x 4 x 3 = 24
