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.


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:

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.