php generate string combinations of missing letters

I have some word lets say BKOO. I need to remove all combinations of missing letters to generate sub words of this initial word. First remove only 1 letter, then n letters to build at least 2 letters words.

So from our example it means to make words like KOO, BOO, OO, BK, BO.

My current algorithm btw says it is possible to generate 7 combinations out of BKOO. (I also include the initial word).

Array
(
    [0] => BKOO
    [1] => Array
        (
            [0] => BKOO
            [1] => KOO
            [2] => OO
            [3] => KO
            [4] => BOO
            [5] => BO
            [6] => BKO
            [7] => BK
        )

)

Note there isnt words like BOK or OOK because that would mean do the reorder, but i dont want to do this. I want just leave letters out of current word, and don't do reorder.

Now problem is, this very slow for lenght like 15. It takes forever. How to speed it up?

function comb($s, $r = [], $init = false) {
  
  if ($init) {
    $s = mb_strtoupper($s);
    $r[] = $s;
  }
  
  $l = strlen($s);
  if (!$s || $l < 3) return [];
  for ($i=0; $i<$l; $i++) {
      $t = rem_index($s, $i);
      $r[] = $t;
      
      $r = array_merge($r, comb($t));
  }
  $ret = array_unique((array)$r);
  return $init ? array_values($ret) : $ret;
}

// remove character at position
function rem_index($str, $ind)
{ 
   return substr($str,0,$ind++). substr($str,$ind);
}

$s = 'BKOO';
print_r(comb($s, [], true));

https://www.tehplayground.com/62pjCAs70j7qpLJj

NERD SECTION:

Interesting note - first i thought i will generate array of some dropping indexes eg, first drop only 1 letter so say drop 0 then 1 etc etc, then 2-combinations so drop 1 and 2, 1 and 3 etc, but then i thought it would be quite difficult to drop N letters out of string at once, so i came with idea that i always drop some letter from the string, and recursively call the function again if you get me, so the next level is one char dropped already and does the drop iteration again. Problem is it is very slow for some reason.

Btw if you have also the math background, what is equation to compute the resulting combinations? To me the rough computation is lets say for 15 letters word 14 * 13 * 12 or at least it does such iteration, but that would be milions of combinations and obviously its not like that even for shorter words like 8.

Thanks.