When you solve permutation problems, you can use various methods depending on what information is given in the question. The flowchart on the previous page will guide you through this information and allow you to determine the appropriate method for solving each question.
Lesson 2D introduces questions in which order does not matter. After studying these, you will be expected to determine which type of problem you have before solving it. If you are unsure why any question in this lesson is identified as a permutation, contact your teacher for clarification.
What does a problem from this branch of the flowchart look like? Here is an example:
In how many ways can swimmers finish first, second, and third in a swim meet if ten swimmers are in the race?
This question considers only first, second, and third place finishes, so you will be using three of the ten swimmers to solve the problem. Also, the swimmers are the objects and are not identical because each person is distinct . These two facts indicate this question is in the branch that ends with n P r .
n P r can be read from n objects arrange r objects or from n objects permute r objects but is usually shortened to n permute r . Various notations are used to represent this permutation.
n P r = n P r = P(n,r)
The first notation is most common and is used exclusively throughout this lesson and in your textbook. The other notations are found in Instant Replay videos later in the lesson.
The number of permutations from a set of n different objects where only r of them are used in each grouping is found using this formula:
Example 1 shows how to use this formula to solve the swim race problem.