//
// Program name:  combination_function
// Author:  B. Massingill
//
// This program defines and tests a "combination" function.
//
// Input, output:  see program text
//
#include <iostream.h>
//
// Function name:  combination
//
// Precondition:
//	n is positive and m is positive and m <= n
// Postcondition:
//	return value is "n choose m" -- number of ways of choosing
//		m objects from among n
//
// Note that we don't say what this function does if the precondition
//	is not met.
// So to use this function appropriately, you should be sure to 
//	call it only with n and m that meet the precondition.
//
int combination(int n, int m);
//
// Function name:  factorial
//
// Precondition:
//	n is positive
// Postcondition:
//	return value is n factorial
//
// Note that we don't say what this function does if n is not positive.
// So to use this function appropriately, you should be sure to 
//	call it only with positive n.
//
int factorial(int n);
//
// Main program
//
int main()
{
	int n, m;
	cout << "Enter two positive integers, the second <= the first\n";
	cin >> n >> m;
	if (n > 0 && m > 0 && m <= n)
		cout << n << " choose " << m << " is " << 
			combination(n, m) << endl;
	else
		cout << "Invalid input\n" ;
	return 0;
}
// code for factorial function (see above for function documentation)
int factorial(int n)
{
	int valueToReturn = 1 ;
	for (int i = 2; i <= n; i++)
		valueToReturn *= i;
	return valueToReturn;
}
// code for combination function (see above for function documentation)
int combination(int n, int m)
{
	return factorial(n) / (factorial(m) * factorial(n-m));
}