CodeCogs

Calculates the number of combinations for a given set of data.

Interface

#include <codecogs/statistics/moments/combin.h>

using namespace Statistics::Moments;

double combin(int n, int k)

Returns the number of combinations for a given number of items. Use Combin to determine the total possible number of groups for a given number of items. A combination is any set or subset of items, regardless of their internal order. Combinations are distinct from permutations, for which the internal order is significant. The number of combinations of n items with k items in each combination is given by the following formula:

$C(N,k)=\frac{P(N,k)}{k!}=\frac{N!}{K!(N-k)!}$

(1)

where:

$P(N,k)=\frac{N!}{(N-k)!}$

(2)

Example 1

#include <codecogs/statistics/moments/combin.h>
#include <iostream>
int main()
 {
   double com = Stats::Moments::combin(9, 5);
   std::cout << "The number of combinations is: " << com << std::endl;
  return 0;
}

Output:

The number of combinations is: 126

Parameters

the total number of items.

the number of items in each combination. k must be less than n.

Returns

the number of combinations for a given number of items

Interactive Calculator

Result –