1. Lesson 3

1.1. Discover

Mathematics 30-2 Module 3

Module 3: Permutations, Combinations, and the Fundamental Counting Principle

 

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 a subset of them? Remember a subset contains only some of the elements of the set.

 

Try This 1

 

Go to the Permutations gizmo at Learn Alberta.

 

 

This is a play button for Permutations.

 

Screenshot reprinted with

permission of ExploreLearning

  1. Change the “Number of tiles in box” and “Number of draws from box” to complete a chart similar to the following. 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

     

    Do not list.

    4

    3

     

    Do not list.

    4

    2

     

    Do not list.

    4

    1

     

     

    5

    5

     

    Do not list.

    5

    4

     

    Do not list.

    5

    3

     

    Do not list.

    5

    2

     

    Do not list.

    5

    1

     

     
  2. In Lesson 2 you always determined the number of permutations using the entire set of objects. What was different in this activity as compared to the permutations you calculated in Lesson 2?
  3. Describe any patterns you noticed in the chart. Explain why the patterns might exist.
  4. Do AEI and IEA each count as one possible permutation? Did the order that the tiles were arranged in affect the number of possible permutations?

course folder Save your responses in your course folder.

The order the tiles are arranged in does matter. AEI is a different permutation from IEA.