It's not that hard of a calculation, with the exception of following the Colony / Shelters rule properly.
C = total number of kingdom card piles
T = total number of kingdom card piles costing
E = total number of events + landmarks
Non-Young Witch games:
((C-1) Choose 10) +
((C-1) Choose 10) * (E) +
((C-1) Choose 10) * (E Choose 2)
Young Witch games:
(C-1) Choose 9) * T +
(C-1) Choose 9) * T * (E) +
(C-1) Choose 9) * T * (E Choose 2)
An upper bound would be to multiply it by 4 for the Shelters / Colonies. Also, my calculation isn't accounting for the fact that there's fewer bane choices when the Kingdom already has cards that cost
*Edit* I suppose you need to calculate Kingdoms that contain Obelisk separately; those ones are just multiplied by 10.