Lesson 2
1. Lesson 2
1.4. Discover
Module 8: Permutations, Combinations, and the Binomial Theorem
Discover
You have used factorial notation to determine the number of permutations of n items taken n at a time, but what happens if you are only going to arrange some of the items?
Try This 1
Go to “Permutations.” You will explore the number of permutations when all items are chosen and when only some of the items are chosen.
Screenshot reprinted with permission of ExploreLearning
- Change the “Number of Tiles in Box” and “Number of Draws from Box” to fill a chart similar to the following one. Use the “List” or “Tree” tab to view the possible permutations.
Number of Tiles in Box
Number of Draws from Box
Total Number of Possible Permutations
List Possible Permutations
2
2
2
AE, EA
2
1
2
A, E
3
3
3
2
3
1
4
4
Don’t list
4
3
Don’t list
4
2
Don’t list
4
1
5
5
Don’t list
5
4
Don’t list
5
3
Don’t list
5
2
Don’t list
5
1
-
Describe any patterns you noticed in the chart. Explain why the patterns might exist.
-
Would AEI and IEA each count as one possible permutation? Did the order the tiles were arranged in affect the number of possible permutations?
