Drawing blanks and determining the number of ways they can be filled in works well when a small number of items is being arranged. But if a large number of items needs to be organized, drawing blanks can be a tedious and time-consuming method.

 

For example, 100 people line up for 50 audition spots on a talent show. In how many ways can the 50 audition spots be filled? You could draw 50 blanks and work to fill in the blanks, but you also know a formula that can be used to determine the number of permutations.

 

There are a total of 100 items, so n = 100.

 

From these 100 items only 50 are taken at a time, so r = 50.

 

Use the formula to calculate the number of permutations.

 

If you recall, 69! is the largest factorial your calculator can calculate. To get around this issue, many graphing calculators are programmed to determine the number of permutations using a different notation, nPr, where

• n is still the total number of objects
• r is the number of objects you want in each arrangement

To calculate you would use 100P50 to calculate the number of permutations.

 

Investigate how to perform the permutation calculation on your calculator. You may need to reference the calculator’s guide or ask your teacher for assistance.

 

If the value of n and r are relatively small, you may solve nPr by simplifying the factorials.