How many planes would by formed by n non-collinear and non-coplanar points?
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Since three non-collinear points define a plane, this is just the number of cominations of three points we can choose from the n, which is $\displaystyle \binom{n}{3}=\frac{n!}{3!(n-3)!}=\frac{n(n-1)(n-2)}{6}$. -Kevin C.
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