One of the best methods for calculating the binomial coefficient I have seen suggested is by Mark Dominus. It is much less likely to overflow with larger values for N and K than some other methods.
public static long GetBinCoeff(long N, long K)
{
// This function gets the total number of unique combinations based upon N and K.
// N is the total number of items.
// K is the size of the group.
// Total number of unique combinations = N! / ( K! (N - K)! ).
// This function is less efficient, but is more likely to not overflow when N and K are large.
// Taken from: http://blog.plover.com/math/choose.html
//
long r = 1;
long d;
if (K > N) return 0;
for (d = 1; d <= K; d++)
{
r *= N--;
r /= d;
}
return r;
}