UVA sloved: problem number: 369 - Combinations

question:

                                          Combination

Computing the exact number of ways that N things can be taken M at a time can be a great challenge when N and/or M become very large. Challenges are the stuff of contests. Therefore, you are to make just such a computation given the following:


GIVEN:

Compute the EXACT value of:

You may assume that the final value of C will fit in a 32-bit Pascal LongInt or a C long.

For the record, the exact value of 100! is:

     93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,
        468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,
        697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000

Input and Output

The input to this program will be one or more lines each containing zero or more leading spaces, a value for N, one or more spaces, and a value for M. The last line of the input file will contain a dummy N, M pair with both values equal to zero. Your program should terminate when this line is read.

The output from this program should be in the form:


N things taken M at a time is C exactly.

Sample Input


     100  6
      20  5
      18  6
       0  0

Sample Output
100 things taken 6 at a time is 1192052400 exactly.
20 things taken 5 at a time is 15504 exactly.
18 things taken 6 at a time is 18564 exactly.

_____________________________________________________________

solution:


#include <iostream>
#include <iomanip>
using namespace std;


long double factorial (long double n)
{
    long double x = 1;
    for (long double i = 2; i <= n; i++) { x*= i;}
    return x;
}
int main ()
{
    long double m, n;
 while (cin >> n >> m && m!=0 && n!=0)// && m<=n && 5<=n<=100 && 5<=m<=100)
    {
        long double f = (factorial(n))/(factorial(n-m)*factorial(m));
        cout << n << " things taken " << m << " at a time is " << fixed << setprecision(0) << f << " exactly." << endl;
    }
}