Combinatorial Examples

	Without Repetition	With Repetition
Combinations pick k from n where k < n Order does not matter	$\frac{n!}{(n-k)!k!}$ C# Recursive Example C# Iterative Example	$\frac{(n+k-1)!}{(n-1)!k!}$ C# Recursive Example
Permutations arrange all elements Order matters	$n!$ C# Recursive Example C# Iterative Example	$\frac{(\sum n_i)!}{(\Pi(n_i!)}$ C# Recursive Example
Variations arrange and pick k from n where k < n Order matters	$\frac{n!}{(n-k)!}$ C# Recursive Example	$n^k$ C# Recursive Example C# Iterative Example

Without Repetition

With Repetition

Combinations
pick k from n where k < n
Order does not matter

$\frac{n!}{(n-k)!k!}$

$\frac{(n+k-1)!}{(n-1)!k!}$

Permutations
arrange all elements
Order matters

$n!$

$\frac{(\sum n_i)!}{(\Pi(n_i!)}$

Variations
arrange and pick k from n where k < n
Order matters

$\frac{n!}{(n-k)!}$

$n^k$