Arithmetic & Number Theory
Binomial Coefficient
Ways to choose k items from n.
Formula
Formula
C(n,k) = n!k!(n−k)!
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| n | total items | integer (ℤ) | — | input |
| k | chosen items | integer (ℤ) | — | input |
Try it yourself
Interactive calculator
Worked examples
Example 1
Givenn = 10, k = 3
Result120
Example 2
Givenn = 52, k = 5
Result2598960