How to use this calculator
Choose whether order matters and repetition is allowed.
Formula and method
P(n,k)=n!/(n−k)!; C(n,k)=n!/[k!(n−k)!]; ordered repetition n^k; unordered repetition C(n+k−1,k); multinomial n!/Π nᵢ!.
Worked example
Five items choose two unordered without replacement: C(5,2)=10.
Assumptions and supported scope
n,k≤1000. Multinomial ≤100 groups and total ≤1000. Results are exact decimal integers and can be long.
Method references
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