That doesn't take into account repeated letters. You actually want the number of 7-combinations of the multiset { A * 5, B * 3, C * 4, ... } or whatever the let

That doesn't take into account repeated letters. You actually want the number of 7-combinations of the multiset { A * 5, B * 3, C * 4, ... } or whatever the letter frequencies are. That's for the first draw from the bag.