Binomial_Coefficient — Arithmetic

Returns the binomial coefficient using the factorial function.

Interface

#include <codecogs/maths/combinatorics/arithmetic/binomial_coefficient.h>

using namespace Maths::Combinatorics::Arithmetic;

inline double binomial_coefficient(int n, int k)

The binomial coefficient $\left ( \begin{array}{c}n\\k \end{array} \right )$ is the number of ways to pick k unordered outcomes from n possibilities. This is also known as combination number, $_{n}C_k$. It is defined as:

$$_nC_k \equiv \left ( \begin{array}{c}n\\k \end{array} \right ) \equiv \frac{n!}{k!(n-k)!}$$

(1)

Parameters

number of possibilities

number of outcomes

Returns

the binomial coefficient C(n, k), i.e. n! / (k!(n-k)!)

Interactive Calculator

Result –