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

Well I am not clever enough to comprehend ikegami's solution but I was able to convert it to Javascript for my purposes. I don't know how it works but it is brilliant!

lists = [["a","b"],["x","y"],["1","2","3"]] 

function factorPermutations(lists) {  

permutations = []
$iter = 0;

while (1) {

    $num = $iter++;
    $pick = []; 

    for (l in lists) {
        $r = $num % (lists[l].length );
        $num = ($num - $r) / lists[l].length;
        $pick.push( lists[l][$r])
    } 
    if ($num > 0) break;

    permutations.push( $pick);
}
    return permutations
} 

console.log(factorPermutations(lists))

Yeah, I left some of the $ signs on variables from the PHP version.