# Lesson: Permutations

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### Lesson Objective

We will be able to determine the permutations for a set of objects and determine probabilities.

### Lesson Plan

Do Now: (5 minutes)

1) Use the fundamental counting principal to determine how many different sandwiches can be made if there are 3 choices of bread, 4 choices of meat, and 4 choices of cheese if one of each is chosen.

2) Mr. Fiori has â…” gallon of paint. He pours the paint into 3 plastic bottles so that each bottle holds the same amount. How much paint does each bottle hold?

3) Find P(not a prime number) with one roll of a number cube.

Direct Instruction: (20 minutes)
Yesterday  we talked about the Fundamental Counting Principle. Today we are going to move into permutations. Let’s see if we can figure out how permutations work.

Fill in the following table with students.

Ex. In how many orders could we read n books?
 n show the orders count 1 2 3
Complete the table as a class. In the second column students will show a sample space for the different ways that the books can be read. The third column will be the total from the sample space. Walk through the multiplication for the third column. How many books did we have to choose from to read first? Second? Etc.   Last column will show factorial- ask a student if they know how to show how write our multiplication problems in a shorter way.

Permutations are an arrangement of items from the same group in which order is important.

Permutations are different from the Fundamental Counting Principle because
Permutations pull from the same group repeatedly, FCP problems pull from different groups.

Ex. In how many ways can president and vice-president of the class be elected from 25 students?
Ask students how this problem is different from the first. (We aren’t using all students- we used all of the books)

_________ x _________

Permutation Notation:
The first number is the number of choices. The second is the number of decisions.

Ex. The finals of the Northwest Swimming League features 8 swimmers. If each swimmer has an equally likely chance of finishing in the top two, what are the odds that a swimmer will finish in the top 2?

Guided Practice: (10 minutes)
Permutations guided practice

Assessment: (10 minutes)
Permutations work-out

### Lesson Resources

 permutations guided practice   Classwork 978 Permutations work out   Assessment 727 G9 4 notes   Notes 565