hacky solution :) 
## usage example:
## program.pl -cards 5 -holes 3

use strict;
use warnings;

use feature 'say';

use Getopt::Long;
use Algorithm::Combinatorics 'combinations';

main();
exit 0;

sub main {
    GetOptions(
        'cards=i' => \my $cards,
        'holes=i' => \my $holes
    );
    die unless $cards and $holes;
    # TODO: more robust error checks
    # for now let's just assume that the user is sane :)

    $cards -= $holes;

    my $tot = $cards + $holes - 1;
    my $combos = combinations( [ 0 .. $tot - 1 ], $cards );

    while ( my $combo = $combos->next() ) {
        my $hack = '0' x $tot;    # total hack! :)

        for my $c (@$combo) {
            substr( $hack, $c, 1, '1' );
        }

        say join ', ', map length() + 1, split /0/, $hack, -1;
    }
}

[download]
example: 
$ perl buk.pl -c 12 -h 7 | wc -l
462

[download]

In reply to Re^2: Combinatorics problem. by Anonymous Monk
in thread Combinatorics problem. (Updated with more info.) by BrowserUk

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