Permutations and Combinations 
 Section 8.6  
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for Factorial, Permutations and Combinations calculator
Lets say 3 people (Andy, Betty, and Clark) compete in a running race. How many different outcomes are possible? 
This a permutation because order is important.  
There 6 different
outcomes possible.


Solve 
Step 
Spot Check 


Permutation Formula  
Take 3 objects from 3 objects 
P(n, n) = n! 

You can also view this problem as 3! = 3 × 2 × 1 = 6. That is, how many different ways can 3 objects be arrangement? 


There are 3 choices for the first spot. That leaves 2 choices left for second spot. After the first 2 spots are chosen, there is 1 left for the 3rd spot.  

5 people are standing in a line. How many different outcomes are possible? 
[Solution] 


In how many ways can you select a committee of 3 people from a group of 12 members? 
This is a combination because the 3 person committee are not ordered.  
Solve  Step 
Combination Formula  
You can cancel the 9!'s  
C(12, 3) = 220 
220 different 3 people committees 

In how many ways can you select a committee of 4 people from a group of 10 members? 
[Solution] 


In how many ways can you select a committee of 3 people from a group of 12 members? The committee members consist of a chairperson, treasurer and a secretary. 
This
is a permutation because the 3 person committee is ordered
because each person has a position. 

Solve 
Step 
Permutation Formula  
You can cancel the 9!'s  
P(12, 3) = 1320 
1320 different 3 person committees 

In how many ways can you select a committee of 4 people from a group of 10 members? The committee members consist of a chairperson, treasurer, officer, and a secretary. 
[Solution] 


A women has 4 blouses, 3 skirts and and 5 pairs of shoes. Assuming the woman does not care what she looks like, how many different outfits can she wear? 
Solve  Step  
4 × 3 × 5 = 60 
Use the Multiplication Principle  Click here  
She has 4 × 3 × 5 = 60 different outfits. 


License plates for cars have to be unique. If a license plate contains 6 characters consisting of 2 letters followed by 4 digits example: QW2354,

[Solution] 


Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada