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The number of triangles that can be formed with 10 points as vertices n of them being collinear is 110, then n= a)3 b)5 c)6 d)4

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Well, we can start with the case of n=0 to give us some intuition, since n=0 will be the maximum number of triangles that can be formed. For the special case n=0, the formula for the number of triangles is simply \(\large{10\choose3}=120\). To go from there, think about how many triangles are ruled out when you add collinear points.

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Any triangle can be formed by choosing 3 points out of the 10. Now this can be done in three ways: 1) Take three non co-linear points. 2) Take one co-linear points and twq points from the left over 10-n points. 3) Take two co-linear points and one of the non-colinear points.

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