How many triangles can be formed from the given points?

A man exploring the ancient Pyramids of Egypt while on vacation stumbled across a secret room. He sneaked away from the tour group and explored the room. He found a dusty lamp and picked it up. While he wiped the dust off the lamp a genie appeared in a puff of smoke.
"For freeing me from my prison, I will grant you a wish, what will it be sire?"
The man thought for a moment, then said, "I want a spectacular job, a job that no man has ever succeeded at or has ever attempted to do."
"Allah Ka Zam!" said the genie. "You're a housewife!"