I have $n$ points in space, no $4$ of which are coplanar. How many distinct planes are determined by these $n$ points?
My thoughts: 3 noncollinear points determine a plane. Therefore, it is C(n,3)?
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3Yes. $!!!!$ – Travis Willse May 04 '15 at 12:56
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But if I change the question ,say, 4 points can be coplanar.Is the answer :C(n,4)? – JimfyWinsy May 04 '15 at 16:07
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No, and worse, if we allow coplanar tetrads of points, the count depends on their configuration. For four coplanar points, there is only $1$ distinct plane; for four noncoplanar points there are, by your formula $C(4, 3) = 4$ planes. – Travis Willse May 05 '15 at 04:35