Here we go.
For the 3 letter case. Number of combinations = 26*26*26, since letters can be repeated
For the 2 leter case 26*26
For 1 letter case 26
Add em up to get answer choice E.
I arrived at E the same way as you, but I have a doubt.
In the two letter combos for example, you cannot distinguish between the two "BB"s. So, there's effectively only one BB. So, you lose 26 two letter combos this way. The same logic for the three letter combos as well.
So, I'm guessing that the answer is something smaller than E, probably D