Question

How many triangles can be formed with 11 points on a plane

Answer 1

In order to answer this question satisfactorily, we must assume that no three points out of the eleven are collinear.

Once we have done this, the problem reduces to finding how many different subsets of three elements are in the powerset of a set with eleven distinct elements. More concisely, we are looking for 11 choose 3, or \(\left(\begin{matrix}11 \\ 3\end{matrix}\right)\).