Combination Calculator
Combination Calculator lets you unordered selections equal n! / (r! × (n−r)!). Enter your own values or load the worked example.
- Copy or download the computed result
- Adjust total items
- See the processing method and limits
Method and calculation
Unordered selections equal n! / (r! × (n−r)!).
Inputs and settings
Combination Calculator accepts Total items (minimum 0, maximum 1000); Items selected (minimum 0, maximum 1000).
Worked example
Combination Calculator example — Total items: 10; Items selected: 3. Computed output: { "combinations": "120" }
Output and limitations
A committee has no internal ordering: selecting Ana then Ben represents the same membership as Ben then Ana. Dividing by the selected members’ factorial removes these duplicate arrangements. The calculator assumes sampling without replacement and reports an exact whole-number count.
Technical references: JavaScript numerical operations
Combination Calculator FAQs
Combination Calculator applies the following rule to your input: Unordered selections equal n! / (r! × (n−r)!). The worked example on this page uses the same processor as the result button.
Combination Calculator has these boundaries: Use finite inputs. Results use double-precision arithmetic. Start by checking the total items field against the units or format shown.
Combination Calculator provides this sample: { "combinations": "120" }. Use the sample button to reproduce it, then replace the inputs with your own values.