Calculate C(n, k) instantly — exact results for any n and k
Inputs
Result
Formula
C(10, 3) = 10! / (3! × 7!) = 120
Digit count: 3 digits
Reference
Common values
| Expression | Value | Context |
|---|---|---|
| C(52, 5) | 2,598,960 | 5-card poker hands from a 52-card deck |
| C(49, 6) | 13,983,816 | 6/49 lottery combinations |
| C(10, 5) | 252 | Choosing 5 from 10 |
| C(20, 10) | 184,756 | Choosing 10 from 20 |
| C(100, 2) | 4,950 | Pairs from 100 items |
The binomial coefficient calculator computes C(n, k) — read "n choose k" — the number of ways to select k items from a set of n items where order does not matter. Using exact BigInt arithmetic, it handles values far beyond what floating-point allows, displays the full formula, and optionally renders Pascal's triangle with your result highlighted.
A binomial coefficient C(n, k), also written nCk or "n choose k", counts the number of ways to pick k items from n distinct items when order does not matter. It equals n! divided by (k! times (n minus k)!).
C(n, k) equals 0 when k exceeds n, because you cannot choose more items than are available. The calculator shows this result with an explanatory note.
The tool uses JavaScript BigInt arithmetic, which provides exact integer results regardless of size — no floating-point rounding errors. C(100, 50) for example has 29 digits and is computed correctly.
Pascal's triangle arranges binomial coefficients in rows where each entry is the sum of the two entries directly above it. Row n of Pascal's triangle contains C(n,0) through C(n,n). The calculator can display the triangle with your specific C(n,k) value highlighted, for n up to 14.