Someone have calculated how many theoric different character combiniation are possible?
4 - wizard, sorcerer, witch, arcanist
the rest are not protagonist material
Yep. But you also need to take subclasses, races and mythic paths into account (considering feats and other stuff would generate a ridiculous large number).
That said, Arcanist has 5 subclasses. Sorc, 6. Witch, 4. Wiz, 4. There are also 12 races to chose from(human, elf, manlet, gnome, hobbit, half elf, half orc, aasimar, tiefling, oread, dhampir and furry), and 9 mythic paths(zealots, demons, i wanna be a dragon, azatas, aeon, cheater, papa bones and filthy swarm). Without considering that some subclasses require that you play as a manlet from the merchants guild(gnome), we have 19 subclasses(6+4+4+5) * 9 mythic paths * 12 races, or 2052 combinations of arcane main character.
Those who commit the heresy of not playing this game as a arcane caster, probably can expect a much larger number of race/class/mp combinations.
EDIT : Forgot to take base classes and the specializations for wiz, patrons for witches, blodlines for sorc and etc.