//
// lotto2.cpp
// CSC 215
// John Rogers
//
// This program computes the odds of 
// winning the lottery.
//

#include <iostream.h>

long factorial(long n);
long falling(long n, long k);

int main()
{
    long numberOfBalls;
    long numberChosen;
    long odds;

    cout << "How many balls are in the game? ";
    cin >> numberOfBalls;

    cout << "How many balls are chosen from that? ";
    cin >> numberChosen;

    odds = falling(numberOfBalls, numberChosen) / 
           factorial(numberChosen);

    cout << "The odds of winning are " << odds 
         << ":1." << endl;

    return 0;
}

//
// This computes n!.
//
long factorial(long n)
{
  long index;
  long answer = 1;

  for (index = 1; index <= n; index++) {
    answer *= index;
  }
  return answer;
}

//
// This computes n to the falling k power
// In mathematical text, we write 
// "n to the falling k power" as n^k_.  Its
// definition is: 
//
//   n^k_ = n*(n-1)*(n-2)*...*(n-k+1)
//
long falling(long n, long k)
{
  long index;
  long answer = 1;

  for (index = n-k+1; index <= n; index++) {
    answer *= index;
  }
  return answer;
}