# combination and permutation

In mathematics, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the elements of the subset can be listed in any order. In a permutation, the elements of the subset are listed in a specific order.

All data sets have a finite number of combinations as well as a finite number of permutations. This makes them useful for calculating probability for complex events. The more elements contained in a set, the greater the number of possible permutations and the smaller the probability that a specific permutation will occur.

The common notations used for combination and permutation are as follows:

The number of combinations of n units

C(n,r)= n!

(n−r)!r!

The number of permutations of n units considered r at a time is:

P(n,r)= n!

(n−r)!