Arithmetic & Number Theory

Binomial Coefficient

Ways to choose k items from n.

Formula

Formula
C(n,k) = n!k!(n−k)!

Variables

SymbolDefinitionType & rangeUnitsRole
n total items integer (ℤ) input
k chosen items integer (ℤ) input

Try it yourself

Interactive calculator
Result

Worked examples

Example 1
Givenn = 10, k = 3
Result120
Example 2
Givenn = 52, k = 5
Result2598960