Combination Calculator
C(n,r) = n! / (r!(n−r)!). Click any i for detail.
n and r
n
i
n
Size of the set. Need n ≥ r ≥ 0. |
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|---|---|
r
i
r
How many you pick. |
How to use this calculator
- Enter n (set size) and r (pick size).
- Confirm 0 ≤ r ≤ n.
- Read nCr combinations and nPr permutations alongside.
- Use combinations when order does not matter.
Results explained
Combinations count unordered subsets. nCr = n! / (r!(n−r)!). Large n may lose integer precision in JavaScript.
Quick reference: nCr
C(10,3) = 120 unordered triples from 10 items.
| Item | Detail |
|---|---|
| nCr | order ignored |
| nPr | order matters (shown for compare) |
| C(n,0) | always 1 |
| C(n,n) | always 1 |
Lottery odds need both combinations and ticket rules.
How the estimate is built
C(n,r) = n! / (r! × (n−r)!).
Example scenario
C(10,3) → 120.
FAQ
When do I use permutations instead?
When order matters, like podium finishes or PIN digits.
Is C(10,3) the same as C(10,7)?
Yes. Choosing 3 to keep equals choosing 7 to leave.
Why does huge n look wrong?
Factorials overflow JS number precision; keep n modest on this page.