Lesson 7: 5.7 The Multiplication Counting Principle and Permutations
Duration of Days: 3
Lesson Objective
Students will be able to calculate the number of possible outcomes using the Fundamental Counting Principle and determine the number of permutations of n objects taken r at a time.
If you have 3 shirts, 2 pants, and 4 hats, how many outfits can you make? (Why do we multiply?)
In a race, does the "order" of the top three finishers matter? How does that change our counting?
Multiplication Counting Principle
Factorial (!)
Permutation
nPr
HSS-CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
The SAT Math section occasionally includes "Counting" problems (e.g., "How many different 4-digit passcodes are possible?").
Before we find the probability, we need to know the total size of the the sample space. This section teaches students how to count massive numbers of outcomes quickly.
The Problem: A license plate consists of 3 letters followed by 4 digits.
Task: How many different license plates are possible if repetitions are allowed? How many if repetitions are not allowed?
Students struggle to decide if order matters. (Permutations vs Combinations)
Before introducing the nPr formula, have students use "slots" for every problem.
Example: To arrange 3 books from a shelf of 10, draw three blanks: __ * __ * __.
Ask: "How many choices for the first slot?" (10). "Since one is gone, how many for the second?" (9).
Teacher assigns examples from the textbook and other resources.
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