First of all, what is considered in America to be "Brazilian jiujitsu" is a false claim. Gracies, have started the "Gracie jiujitsu" are actually formally trained in judo kodokan only. Helio Gracie was a 6th dan in judo, at his peek. I forget what rank his older brother was, but he also was trained in judo only. In Brazil there is no BJJ or Brazilian jiujitsu, and that is an American invention. If Brazilians would claim jiujitsu as brazilian it would be "jiujjitsu Braziliero" or "jjb".
Second MMA is not a sport but a term used to describe athletes that compete and train in multiple sorts, but are not restricted to any specific combination. A karateka-judoka, boxer-wrestler or boxer-karateka, and judoka-wrestler are qualified to be described as MMA fighters, and does not have to be only striking and grappling combinations. There is no MMA manual, or single technique that can be claimed as MMA technique. Any gym that claims to teach MMA is actually teaching some striking sport and some grappling sport. If we exclude false claims, people that quit before they reach any rankings, people that never compete, people that spar with friends in the back yard or fight on the street once every 6 months, and people that cant grasp the concepts at all, we are left with a small number of actual people that do train in Gracie jiujitsu long enough to reach even blue belt rank, and even less actual MMA athletes. However there is a large number of real practitioners, that do not claim to be MMA fighters but according to definition they practice mostly one martial art and reach expert level then cross train in another just for good measure, and qualify to be labeled as MMA fighters.