I'll skip the data reading... With the data in memory, it would go like this:

#!/usr/bin/perl

use warnings;
use strict;

my $src = [['A', 'B', 'C', 'D'],['P', 'Q', 'R'],['1', '2', '3', '4', '
+5']];

my $products = [''];
for my $level (@$src) {
    my $old_products = $products;
    $products = [];
    for my $prefix (@$old_products) {
        for (@$level) {
            push(@$products, "$prefix$_");
        }
    }
}

print "$_\n" for @$products;
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Update: That's merely to help your logic. From the practical view, advices from almut and moritz are probably better.