All courses › Discrete Mathematics › Combinations

Combinations

A combination is a selection where the order does not matter. There are fewer combinations than permutations, because each group of k can be ordered in k factorial ways. The binomial coefficient gives the number.

(nk)=n!k! (n−k)!\binom{n}{k} = \frac{n!}{k!\,(n-k)!}k of n without order
(nk)=(nn−k)\binom{n}{k} = \binom{n}{n-k}symmetry

Symbols

(nk)\binom{n}{k}"n choose k"

Example

A group of 3 out of 10 students:

(103)=10⋅9⋅86=120\binom{10}{3} = \frac{10\cdot 9\cdot 8}{6} = 120.

Ask yourself: is it a new outcome if the same ones swap places? No means combination.
Practise combinatorics for free →

← Permutations · Graphs →

Part of Discrete Mathematics: Combinatorics.