Your self-promotion requires reading the entire file into memory before it can be passed to the module, which makes it kind of inapplicable to problem.

However, if you do have the entire data set in memory, there's a simpler approach than the math theory you use in your module. Rather than iterate the array, consider just drawing at random. If there's a duplicate, then redraw. The larger the set, the less the odds of a duplicate. This scales a lot better than your module, but I admit that does trip up more on sets close to sample size.

It's a lot like how, in gaming, you can fake a d12 by rolling a d20 until you've got a number in range.

use strict;
use Data::Dumper;

my @set = ('a'..'z');
my $size = 3;
my @sample;
my %seen;

while( @sample < $size ){
    my $elt;
    do{
        $elt = int rand(@set);
    }while( $seen{$elt} );

    push @sample, $set[$elt];
    $seen{$elt}++;
}

print Dumper \@sample;
[download]

This example should really have a check, too, to see if the sample size is in the bounds of the set, to avoid looping.