Learners will identify and calculate the number of permutations with repetition.
After completing this tutorial, you will be able to complete the following:
All permutations of a group of identical objects are the same.
Let's use the example of planting three tulips in a box. If all three objects are different, i.e. they have different colors, then there would be 3! (read as "three factorial", or 3 × 2 × 1 = 6) possible arrangements for the tulips.
But if all of the objects are identical, e.g. they are all yellow, then there is no way to tell them apart no matter what order they are planted in. Thus, the number of permutations of the group of three identical yellow tulips would be a single permutation.
The formula used for permutations with repetition is .
Let's take our example and expand on it. Let's say we want to find out the number of different ways that we can plant two identical yellow tulips and three identical red tulips in a flower box.
There are a total of 5! (5 × 4 × 3 × 2 × 1 = 120) possible arrangements of the five tulips. However, since there are two yellow and three red that are identical, we apply the above formula:
There is a total of 10 different ways to plant the five tulips (with two identical yellow tulips and three identical red) in a flower box. This is because the identical ones can be changed around in the order with no difference, because they are identical.
The following key vocabulary terms will be used throughout this Activity Object:
|Approximate Time||25 Minutes|
|Type of Tutorial||Concept Development|
|Key Vocabulary||permutation, permutation with repetition, repetition|