Permutations of an array of arrays of strings

Question

I simply cannot wrap my head around how to solve this problem and after a thorough search on Google with no results, I turn to you with hopes of a solution.

Given the sa

Answer 1

Just for those wanting a PHP translation:

function factor_permutations($lists) {

    $permutations = array();
    $iter = 0;

    while (true) {

        $num = $iter++;
        $pick = array();

        foreach ($lists as $l) {
            $r = $num % count($l);
            $num = ($num - $r) / count($l);
            $pick[] = $l[$r];
        }

        if ($num > 0) break;
        $permutations[] = $pick;
    }

    return $permutations;
}

print_r(factor_permutations(array(array('a', 'b'), array('1', '2', '3'), array('foo', 'bar'))));