“All possible racks,” in such a game, is an infeasible number of possibilities to actually enumerate ... it would take weeks at best, if not months or centuries. But you don’t need to “list them, then count them,” in order to compute the probability of any given draw.
I don't think so. Even assuming the worse-case scenario that the bag has at least 7 copies of each letter, the number of possible ordered racks is at most 26**7, or about 8 billion (we absolutely do not care whether the A that you get is A1, or A2, or A3..., it is just an A). This is admitedly a big number, but you certainly don't need weeks (let alone centuries) to list them all on a computer by the standards of today. And the actual number of racks is in fact much smaller for two reasons: some letters have only possibly two or three copies and that reduces quite drastically the number of actual possibilities, and many racks are actually equivalent (permutations of another one). I do not have enough information on the game to compute everything, but I would be surprised if the number of actually different racks would exceed a couple of millions. So at most a few seconds to enumerate them all on a modern computer.
