Most often, MMA fighters are trained with a good set of both striking, and grappling skills.
It makes a bit of sense. Flashy kicking, and extended acrobatics are at a disadvantage when locked inside a cage against a grappler, who would only need the ground he walks on to fight.
Once you have someone pinned down to the ground, that's where the boxing background can come in handy.
but there are also a lot of mma fighters with mainly jiujitsu or wrestling backgrounds, and it seems like most of the bouts ends with submissions so....