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.

 

1. 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

2. Describe any patterns you noticed in the chart. Explain why the patterns might exist.

3. Would AEI and IEA each count as one possible permutation? Did the order the tiles were arranged in affect the number of possible permutations?