Can you help me understand this math problem...I could figure it out the long way but I think there is a formula that I can use that I'm not remembering:

Question

I have 18 different colors of marbles. I'm going to arrange them in sets of three.
I want to do this 6 times with out any of them ever being in the same set again...like the first time I might have orange, purple, green in one set and so the next time, I don't want there to be a set with any of those three together.
If it doesn't work right with doing it six times, I think it should with 5 times.
Any help?