Lesson 8: 5.8: Combinations and Probability
Duration of Days: 3
Lesson Objective
Students will be able to calculate the number of combinations of n objects taken r at a time and use these counts to solve complex probability problems.
Why is a "Combination Lock" actually a "Permutation Lock"?
How do we use the "Groups" method to find the probability of a specific outcome (like winning the lottery)?
Combination
nCr
HSS-CP.B.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
Combinations are less frequent on the SAT than basic probability, but understanding how to choose "subsets" of a group is useful for advanced data logic questions.
This section combines counting (Combinations) with the definition of probability (Desired/Total).
The Problem: A box contains 20 batteries, 4 of which are defective. If you choose 3 batteries at random, what is the probability that exactly 1 of them is defective?
Calculator Reliance: Students often use the button without understanding what $nCr$ is doing (choosing a subset where order is irrelevant).
Support: Create a "Logic Tree": Does order matter?
Yes --> Permutation.
No -->Combination.
Extension: Introduce the Binomial Coefficient and show how it relates to Pascal’s Triangle
Teacher assigns examples from the textbook and other resources.
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