**What’s the Difference?**

- When the order doesn’t matter, it is a
**Combination**. - When the order
**does**matter it is a**Permutation**.

In other words:

__A Permutation is an ordered Combination.__

__Permutations__

There are basically two types of permutation:

**Repetition is Allowed**: It could be “333”.**No Repetition**: for example, the first three people in a running race. You can’t be first*and*

__1. Permutations with Repetition__

__1. Permutations with Repetition__When a thing has ** n** different types … we have

**choices each time!**

*n*For example: choosing ** 3** of those things, the permutations are:

**n × n × n***(n multiplied 3 times)*

Example: in the lock above, there are 10 numbers to choose from (0,1,2,3,4,5,6,7,8,9) and we choose 3 of them:

__10 × 10 × 10 (3 times) = 10 ^{3} = 1,000 permutations__

So, the formula is simply:

n^{r} |

where is the number of things to choose from,nand we choose of them,rrepetition is allowed, and order matters. |

__2. Permutations without Repetition__

__2. Permutations without Repetition__

In this case, we have to **reduce** the number of available choices each time.