# How do permutations and combinations differ?

Nov 24, 2014

A permutations is an arrangement, so the order of its elements matters; on the other hand, a combination is a subset, so the order of its elements does not matter.

Example

All permutations of two elements from $\left\{a , b , c\right\}$ are:

$a b , b a , a c , c a , b c$, and $c b$

All combinations of two elements from $\left\{a , b , c\right\}$ are:

$\left\{a , b\right\} , \left\{a , c\right\}$, and $\left\{b , c\right\}$

I hope that this was helpful.