Combinations.cpp

/*
 * File: Combinations.cpp
 * ----------------------
 * This program computes the mathematical function C(n, k) from
 * its mathematical definition in terms of factorial.
 */

#include <iostream>

/* Function prototypes */

int combinations(int n, int k);
int fact(int n);

/* Main program */

int main()
{
	int n, k;

	std::cout << "Enter the number of objects (n): ";
	std::cin >> n;
	std::cout << "Enter the number to be chosen (k): ";
	std::cin >> k;
	std::cout << "C(n, k) = " << combinations(n, k) << std::endl;

	return (0);
}

/*
 * Function: combinations(n, k)
 * Usage: int nWays = combinations(n, k);
 * --------------------------------------
 * Returns the mathematical combinations function C(n, k), which is
 * the number of ways one can choose k elements from a set of size n.
 */

int combinations(int n, int k)
{
	return (fact(n) / (fact(k) * fact(n - k)));
}

/*
 * Function: fact(n, k)
 * Usage: int result = fact(n);
 * ----------------------------
 * Returns the factorial of n, which is the product of all the
 * integers between 1 and n, inclusive.
 */

int fact(int n)
{
	int result = 1;
	for (int i = 1; i <= n; i++)
		result *= i;
	return (result);
}