// numeric_function.cpp

#include <algorithm>
#include <numeric>
#include <vector>

#include "tips.hpp"

int factorial( int n );
int teams( int candidate_size, int team_size );

using namespace std;

int main( )
{
   // make a vector with 0, 1, 2, 3, 4, 5
   vector<int> numbers( 6, 1 );
   numbers[0] = 0;
   partial_sum( numbers.begin(), numbers.end(), numbers.begin() );

   // compute the factorial of each number
   vector<int> result( 6 );
   transform( numbers.begin(), numbers.end(), result.begin(),
      factorial );
   tips::print( result, "Factorials of 0-5" );

   // candidates available and team sizes for baseball, basketball,
   // football and soccer
   const int candidate_array[] = { 14, 11, 30, 17 };
   const int team_array[]      = {  9,  5, 22, 11 };
   const int array_length = sizeof( candidate_array )
      / sizeof( candidate_array[0] );

   vector<int> candidate( candidate_array,
      candidate_array + array_length );
   vector<int> team( team_array, team_array + array_length );
   result.resize( array_length );

   // compute the number of possible teams
   transform( candidate.begin(), candidate.end(), team.begin(),
      result.begin(), teams );

   cout << endl
   << "There are " << result[0] << " possible baseball teams\n"
   << "There are " << result[1] << " possible basketball teams\n"
   << "There are " << result[2] << " possible football teams\n"
   << "There are " << result[3] << " possible soccer teams";
}

// n >= 0
int factorial( int n )
{
   int n_factorial = 1;
   for( int i = n; i > 1; --i )
      n_factorial *= i;

   return n_factorial;
}

// num_candidates >= 1,  1 <= team_size <= num_candidates
int teams( int num_candidates, int team_size )
{
   // use double to avoid integer overflow
   double permutations = 1;

   for( int i = num_candidates; i > num_candidates - team_size; --i )
      permutations *= i;

   for( int i = team_size; i > 1; --i )
      permutations /= i;

   return static_cast<int>( permutations );
}

Results

Factorials of 0-5: 1 1 2 6 24 120 

There are 2002 possible baseball teams
There are 462 possible basketball teams
There are 5852925 possible football teams
There are 12376 possible soccer teams