Probability

Permutations is an arrangement of members into a sequence or linear order.

 $_nP_r=\frac{n!}{\left(n-r\right)!}$  

where n is total number of objects in set

where r is number of choosing objects in set

Determines the number of possible arrangement in a collection of items

 $_nC_r=\frac{n!}{r!\left(n-r\right)!}$  

where n is total number of objects in set

where r is number of choosing objects in set

The order of the elements

In permutations, we care about the order

AB is not the same as BA

In combinations, the order doesn't matter

AB is the same as BA