Permutation and Combination

Permutation

Ordered selection of items from a given set is called permutation.

Combination

Selection of items from a given set is called combination.

Example

For the given set: [1, 2, 3]:

Combinations of size 2 (³C₂):

[1, 2]

[1, 3]

[2, 3]

Permutations of size 2 (³P₂):

[1, 2]

[2, 1]

[1, 3]

[3, 1]

[2, 3]

[3, 2]

Permutation

Without Repetition

ⁿP_r = n! (n − r)!

n	: Total number of items to choose from
r	: Number of items to choose

With Repetition

ⁿP_r = n^r

Combination

Without Repetition

ⁿC_r = n! (n − r)! r!

With Repetition

ⁿC_r = (r + n − 1)! (n − 1)! r!