Section 8.3

Probability with Permutations and Combinations

In sections 8.1 and 8.2, you learned about counting objects using the Multiplication Principle, permutations, and combinations. With these strategies, we are able to count the number of different license plate numbers or ways to select lottery numbers. In this section you’ll go one step further and use these strategies to find probabilities.

The key to finding these probabilities is an assumption. We will assume that the outcomes in whatever event and experiment we are considering are equally likely. This will enable us to calculate the probability of an event by counting the number of outcomes in it. Specifically, we’ll find the probability of an event E from a sample space S with

where n(E) and n(S) are the number of outcomes in E and S. This will helps us to calculate the likelihood (or unlikelihood) of events such as winning the lottery jackpot or detecting a defective product on a production line.

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