I don't think you're correct. A discrete distribution can be defined for any number of values. Linux, which is the subject of the paper, uses a discrete distribution too.
Ok, that's fine, you just want to use 1s and 2s (though it would have been more obvious if you'd just used 0s and 1s :) ).
In that case, you don't have as many 11s and 22s as 12s and 21s (I'm ignoring the commas since they're irrelevant).