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Permutations

A permutation is an arrangement where the order matters. The number of ways to arrange n things is n factorial. If you only choose k of them in order, there are fewer possibilities.

n! = n\cdot(n-1)\cdots 2\cdot 1

all n in order

P(n,k) = \frac{n!}{(n-k)!}

k of n in order

Symbols

$n$	number of things
$k$	number chosen

Example

Gold, silver and bronze among 8 runners:

$P(8,3) = 8\cdot 7\cdot 6 = 336$ .

By definition 0! = 1.

Practise combinatorics for free →

← The multiplication principle · Combinations →

Part of Discrete Mathematics: Combinatorics.