That's a hard question to answer! And the number that exist is different from the number possible. The number that exists is changing all the time (like taking a snake which is homozygous for 4 traits, adding another trait to it, and creating a new combination which has not been created yet....or discovering new traits such as the recently produced palmetto cornsnake). The possibility was always there for that combination to be created, but it wasn't yet.
The calculation I believe blutenangel is talking about is the combination calculation (where order is not important and repetition is not allowed...so hypo lavender is the same as lavender hypo). If you know factorials, the formula is n!/r!(n-r)! where n is the number possible to choose from, and r is how many to choose. If you go to ian's vivarium there are 20 single trait recessive genes. If you want to take out stargazer that is 19. Then there are 2 dominant genes if you want to include buf and tessera. So lets just pretend for the sake of argument that you picked 20 as the number of traits to choose from (n=20). You would have to calculate the combination using r=1, r=2, r=3, and add them together. (r=1 means you only choose 1 trait out of 20....the combination of 20 choose 1 would equal 20 because you could choose amel OR hypo OR stripe etc...). Then you would do the combination of 20 choose 2, as in hypo lavender, or hypo amel, or hypo stripe etc.... and amel stripe or amel caramel or amel motley etc...There are 190 possible combinations if you choose 2 morphs out of 20). Then do 20 choose 3, 20 choose 4 up to 20 choose 20. (20 choose 20, by the way, would mean a snake that has all 20 traits out of the 20 possible....which would equal 1...but obviously does not currently exist in the cornsnake world. And I doubt it ever would because I would assume it would probably be just a plain white muddled mess). But, anyway, so adding together all those combinations you'd get 1,048,575 possible combinations. Then you also need to add in the wild type/locality/selectively bred stuff (lets just say normal, okeetee, miami, keys...so 4...the number is actually way more than this but I am just using 4 as an example) and the possibilities are 1,048,579.
Wow, that was long, boring, and too much math. But with using 20 traits to choose from that is the number of possible outcomes.
Of course, most of those possible outcomes do not currently exist...and as I stated probably never will. So for simplicities sake I'd probably just count up all the possiblities on ians vivarium, though those probably aren't all the ones that currently exist, there are bound to be a few missing.
I think it's hard to answer the "most wanted" corn. Currently in terms of rarity and people probably wanting to own one I'd say the newly produced palmetto, just because it is so different and so rare. In terms of popularity and ownership I'd say the normals/amel/anery/snow are probably the most abundant and commonly kept.
