in reply to
Fastest way to calculate hypergeometric distribution probabilities (i.e. BIG factorials)?

You should compute log gamma. There are formulas that compute it very quickly and accurately, for example: Malloc with Inline::C.
By the way gamma(n+1) = n! for positive integer n. (Some responders said gamma(n) = n!, which is wrong).

**Update:** Here is some code (perl version of gammln is from Re^4: Challenge: Chasing Knuth's Conjecture):

`#!/usr/bin/perl -w
use strict;
sub logfact {
return gammln(shift(@_) + 1.0);
}
sub hypergeom {
# There are m "bad" and n "good" balls in an urn.
# Pick N of them. The probability of i or more successful selection
+s:
# (m!n!N!(m+n-N)!)/(i!(n-i)!(m+i-N)!(N-i)!(m+n)!)
my ($n, $m, $N, $i) = @_;
my $loghyp1 = logfact($m)+logfact($n)+logfact($N)+logfact($m+$n-$N)
+;
my $loghyp2 = logfact($i)+logfact($n-$i)+logfact($m+$i-$N)+logfact(
+$N-$i)+logfact($m+$n);
return exp($loghyp1 - $loghyp2);
}
sub gammln {
my $xx = shift;
my @cof = (76.18009172947146, -86.50532032941677,
24.01409824083091, -1.231739572450155,
0.12086509738661e-2, -0.5395239384953e-5);
my $y = my $x = $xx;
my $tmp = $x + 5.5;
$tmp -= ($x + .5) * log($tmp);
my $ser = 1.000000000190015;
for my $j (0..5) {
$ser += $cof[$j]/++$y;
}
-$tmp + log(2.5066282746310005*$ser/$x);
}
print hypergeom(300,700,100,40),"\n";
`