What’s the Difference?

• When the order doesn’t matter, it is a Combination.
• When the order doesmatter 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

When a thing has n different types … we have n choices each time!

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) = 103 = 1,000 permutations

So, the formula is simply:

 nr where n is the number of things to choose from, and we choose r of them, repetition is allowed, and order matters.

### 2. Permutations without Repetition

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