Combination Calculator
Calculate Combinations
Compute combinations with and without repetition. For n distinct items choosing r without order, combinations without repetition are nCr = n! / (r!(n−r)!), and with repetition are C(n+r−1, r).
About Combinations
A combination is a selection of items where order does not matter. When repetition is not allowed, the number of ways is nCr. When repetition is allowed, the count becomes C(n + r − 1, r).
Formulas
- Without repetition: nCr = n! / (r!(n−r)!)
- With repetition: C(n + r − 1, r)
Use cases
- Lottery: Selecting numbers where order does not matter
- Sampling: Choosing subsets from a population
- Stars and Bars: Distributing identical items into bins (with repetition)