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