One of the many things I love about pool is that every rack I've ever played has been different than every other rack. If I wanted the same game over and over I'd play darts. ;)
Ok you got me... I'm a computer guy, not a mathematician.
The answer to that one is easy though... *all* of the patterns have an equivalent 83% pattern.
I would calculate that as having 10 different available positions... so 1024... in that case your first guess was pretty close!
I am a mathematician. Which I am sure contributes to my love of pool.
2 to the power of 12 = 4096 "different" layouts.
111111000000
111110000001
111100000011...
101010101010...
000000111111
This is also how we measure password complexity btw. Alphabet size to the power of password length...