Permutations and combinations

Permutations

Definition: Arrangement in a definite order of a number of objects taken some or all at a time.

ⁿPᵣ = n! / (n-r)!

where 0 ≤ r ≤ n

Examples:

Properties

Permutations with identical elements

Theorem: Number of permutations of n objects where p₁ objects are of one kind, p₂ objects are of second kind, …, pₖ objects are of kᵗʰ kind and the rest, if any are of different kinds:

n! / (p₁! * p₂! * … * pₖ!)

Uses

Combinations

ⁿCᵣ = n! / [(n-r)! * r!]

Properties

Uses

Result

References