#!/usr/bin/perl -slw
use strict;

my @logfact = <DATA>;

sub hypergeom {
    # There are m "bad" and n "good" balls in an urn.
    # Pick N of them. The probability of i or more successful selections:
    # (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);
}

print hypergeom( 300, 700, 100, 40 );