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# 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 consider r at a time is:

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)!

This was last updated in May 2018

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