A cube has 8 non-coplanar points at the vertices and has 6 faces. This is only a partial answer...3 points determine a plane so there will be many more than 6. Your answer is going to be found by the formula n!/(n-r)! where n=8 and r=3.
That gives: 40320/120 = 336
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3
10!
one
Just one plane.
Exactly one plane in each case.