Co-Tenant RoomMates

[White Glove]

Newbie White Glove here. . .
I am being inundated with application requests from groups of unrelated "roommates" who want to rent my single family home. I'd rather not deal with this situation, though I don't want to discriminate either. I'm requiring that each one fill out an application, and at least one of them has to meet my minimum income requirement of 2.5 times the rent amount, or get a co-signer who can. Am I screwing up here? Can I legally exclude these groups? This is a residential neighborhood of mostly owner occupied single family homes. I envision a "frat house" or "sorority" scenario and I am not feeling good about it.
Thanks,
WG