CalcCombination

CalcCombination[ n, k ] returns the number of ways to choose k items from a set of n items.

Usages

`CalcCombination[ n, k ]`

CalcCombination[ n, k ] returns $\binom{n}{k}$ , the number of ways to choose k items from a set of n items, where the order does not matter. n and k must be non-negative integers with k ≤ n.

Example	in	out
Choose `2` items out of `5`.	`CalcCombination[ 5, 2 ]`	`10`
Choose `5` cards out of `52`.	`CalcCombination[ 52, 5 ]`	`2598960`
There is one way to choose nothing.	`CalcCombination[ 6, 0 ]`	`1`
There is one way to choose everything.	`CalcCombination[ 6, 6 ]`	`1`
Script variables.	`n := 10 k := 3 r := CalcCombination[n, k]`	`r = 120`

Details

Large numbers: the smaller of k and n-k may be at most 100. CalcCombination[ 300, 250 ] is calculated, because 300-250 = 50, but CalcCombination[ 300, 150 ] is left unevaluated.
Lists are not supported: CalcCombination[ {5,6}, 2 ] is left unevaluated. Use Map to apply it to each element.

Invalid input	Result
`CalcCombination[ 6, 7 ]`	Left unevaluated: `k` is larger than `n`.
`CalcCombination[ -6, 2 ]`	Left unevaluated: `n` and `k` must not be negative.

See also: Factorial, Map