This is more of a math question than a Perl question, but I know there are monks with far greater math skills than I, and I hope to pick their brains.

Here's the question:

I have the population figures for several entities. What I am looking for is the probability of a given sample of entities occurring at random. Update: As the first response below demonstrates, I have not been sufficiently clear. I'm looking for a the likelyhood of getting a random sample of seven entities (or however many specified) from the total population represented by the population numbers provided. The order of the sample doesn't matter, just that it has those entities in the stipulated proportions. Some pseudocode:

#!/usr/bin/perl

use strict;
use warnings;

# Population numbers
my $entity1 = 35000
my $entity2 = 41000
my $entity3 = 16000
my $entity4 = 18000
my $entity5 = 21000
my $entity6 = 45000
my $entity7 = 27000
my $entity8 = 10000
my $entity9 = 16000

# Sample constituents

my @sample = ($entity9,$entity9,$entity4,$entity2,$entity6,$entity1,$e
+ntity1)

sub probability {
  # Return the probability of @sample occurring at random based on the
  # populations declared
}
[download]

I would be perfectly happy if someone could show me how to do the math, and I can do the Perl, although seeing how to do the math in Perl would be great too. Thanks.