PHPで単一のセットから特定のサイズのすべての組み合わせを生成するにはどうすればよいですか?

function sampling($chars, $size, $combinations = array()) {

    if (empty($combinations)) {
        $combinations = $chars;
    }

    if ($size == 1) {
        return $combinations;
    }

    $new_combinations = array();
    foreach ($combinations as $combination) {
        foreach ($chars as $char) {
            $new_combinations[] = $combination . $char;
        }
    }

    return sampling($chars, $size - 1, $new_combinations);

}

// Example
$chars = array('a', 'b', 'c');
$output = sampling($chars, 2);
var_dump($output);

array(9) {
  [0]=>
  string(2) "aa"
  [1]=>
  string(2) "ab"
  [2]=>
  string(2) "ac"
  [3]=>
  string(2) "ba"
  [4]=>
  string(2) "bb"
  [5]=>
  string(2) "bc"
  [6]=>
  string(2) "ca"
  [7]=>
  string(2) "cb"
  [8]=>
  string(2) "cc"
}