# choose($n, $k) is the number of ways to choose $k elements from a set
# of $n elements, when the order of selection is irrelevant.
#
sub choose {
    my ($n, $k) = @_;
    my ($result, $j) = (1, 1);

    return 0 if $k > $n || $k < 0;
    $k = ($n - $k) if ($n - $k) < $k;

    while ( $j <= $k ) {
        $result *= $n--;
        $result /= $j++;
    }
    return $result;
}

sub choose_simple {
    my ($n, $k) = @_;
    return permutation($n,$k) / permutation($n-$k);
}