Question: Why were only three predators sent to deal with all the aliens?
Answer: The Aliens are trophies for the Predators, not some ancient mortal enemy. The 3 Predators are a literal hunting party sent for sport. This is why Danny Glover is not killed at the end of Predator 2 as he had managed to hunt and kill a Predator to its death.
Answer: As the film explains, it's part of a "rite of passage" ritual where a small group of chosen predators are sent to hunt xenomorphs to prove themselves worthy. The xenomorphs are the "ultimate prey" for them to hunt. There's only three because that creates more of a challenge for them to overcome. If there were more predators, it wouldn't be as much of a challenge, and thus it wouldn't really prove them to be "worthy."
TedStixon