It would be a total of 32 different combinations. There are 8 starter classes, and 4 starter Eidolons. Classes: Guardian(Melee), Ravager(Melee), Duelist(Melee), Grenadier(Ranged), Gunslinger(Ranged), Sorcerer(Magic), Wizard(Magic), Bard(Magic). Starter Eidolons: Grimm, Alessa, Merrilee, and Serif.
Each class has a total of 4 different combinations from which to choose.
(1 Class x 4 Eidolons) = 4 Class/Eidolon Combos per class.
4 Combinations per class x 8 different classes = 32 Combinations.
And just for kicks, if you were to include the mystery class, It would be a total of 36 combinations. (9 different classes x 4 combinations per class).