choose.cpp

#include <iostream>

template<bool cond, class THEN, class ELSE>
struct if_ 
{
  typedef ELSE type;
};

template<class THEN, class ELSE>
struct if_<true, THEN, ELSE>
{
  typedef THEN type;
};

template<unsigned long long N>
struct unsigned_long_long
{
  static const unsigned long long value = N;
};

template<unsigned long N, unsigned long R>
struct choose
{
  static const unsigned long long value = if_<(N<R),
                                              unsigned_long_long<0>,
                                              unsigned_long_long<(choose<N-1, R-1>::value +
                                                                  choose<N-1, R  >::value)>
                                              >::type::value;
};

template<unsigned long N>
struct choose<N, 0>
{
  static const unsigned long long value = 1;
};

template<unsigned long N>
struct choose<N, N>
{
  static const unsigned long long value = 1;
};

int
main(int argc, char** argv)
{
  std::cout << choose<500, 16>::value << std::endl;
  return 0;
}