Combination calculator (nCr)
Counts the different groups you can choose from n items, such as a committee of 3 people from 10.
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How to use it
- Enter number of items n, items chosen r and repetition.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Without repetition: nCr = n! ÷ (r! × (n - r)!). With repetition: C(n + r - 1, r). Computed with exact integers.
Example
Inputs: Number of items n = 10, Items chosen r = 3, Repetition = Without repetition. Result: Number of combinations: 120; Number of digits: 3; Scientific notation: 120.
Limits and caveats
- n and r are capped at 5000.
- All n items are assumed to be distinct.
Questions about this tool
Why does C(n, r) equal C(n, n - r)?
Choosing r items to keep is the same as choosing n - r items to leave out, so the two counts are always equal.
How many 5 card poker hands are there?
C(52, 5) = 2598960 different hands from a standard 52 card deck.
What are combinations with repetition?
Choices where the same kind can be picked more than once, like 3 scoops from 5 flavours, which gives C(7, 3) = 35.