# include <cstdlib>
# include <iostream>

using namespace std;

int main ( )
//
//  POKER_HANDS2 tries to compute the number of possible hands in 
//  poker.  The correct answer is 52-choose-5 or 52!/(47!*5!).
//  However, it is dangerous to try to compute the factorials
//  first, since 52!, for instance, is a number with at last 40 digits,
//  while the largest legal integer has 10 digits.
//
//  So we replace the CHOOSE function used in POKER_HANDS by a
//  more careful computation called CHOOSE2.
//
{
  int choose2 ( int n, int k );
  int n, k, hands;

  n = 52;
  k = 5;
  hands = choose2 ( n, k );

  cout << "From a deck of " << n << " cards,"
       << " we choose " << k << " cards to form a hand.\n";

  cout << "Assuming the order of the 5 cards doesn't matter,\n";
  cout << "there are " << hands << " different hands we can draw.\n";

  return 0;
}
int choose2 ( int n, int k )
//
//  CHOOSE2 computes N! / (K!*( N-K!)) by
//
//    value = 1 * N/1 * (N-1)/2 * (N-2)/3 * ... (N-K+1)/K.
//
//  This result avoids unnecessary overflow caused by evaluating
//  factorials.
//
{
  int bot;
  int i;
  int top;
  int value;

  value = 1;
  top = n;
  bot = 1;
  for ( i = 1; i <= k; i++ )
  {
    value = ( value * top ) / bot;
    top = top - 1;
    bot = bot + 1;
  }

  return value;
}