CodeCogs

Calculates the multinomial coefficient with the given arguments.

View versions (1)

Interface

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

using namespace Maths::Combinatorics::Arithmetic;

int multinomial(int n, int *factors)

This function calculates the multinomial coefficient with the given arguments $k_1, k_2, \ldots k_n$ ,

$(k_1, k_2, \ldots k_n)! = \frac{(k_1 + k_2 + \ldots + k_n)!}{k_1! k_2! \ldots k_n!}$

(1)

It uses a direct algorithm and so computer overflow may occur during the intermediate calculations, as opposed to the other multinomial component.

References

SUBSET, a C++ library of combinatorial routines, http://www.csit.fsu.edu/~burkardt/cpp_src/subset/subset.html

Example 1

#include <codecogs/maths/combinatorics/arithmetic/multinomial.h>
#include <iostream>
int main()
{
  int factors[4] = {1, 2, 3, 4};
  std::cout << "In the case of the following factors" << std::endl;
  for (int i = 0; i < 4; i++)
    std::cout << factors[i] << "  ";
  std::cout << std::endl << "the multinomial coefficient is" << std::endl;
  std::cout << Maths::Combinatorics::Arithmetic::multinomial(4, factors) << std::endl;
  return 0;
}

Output: In the case of the following factors 1 2 3 4 the multinomial coefficient is 12600

Parameters

the number of arguments

factors

the factors of the multinomial, given as an array

Returns

the multinomial coefficient based on the values of the factors

Multinomial

Interface

References

Example 1

Parameters

Returns