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How many triangles can we form if we draw all the diagonals of a hexagon?

I thought that the answer is $\binom{6}{3}=20$ but this is not the right answer, why?

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    What kind of hexagon? Convex or not? Regular or not? Before using counting tools, we need to know what we are counting.2012-03-09
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    Must the vertices of the triangles coincide with vertices of the hexagon?2012-03-09
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    This is interesting, @Andre considering the type of question I guess it should be convex-regular.2012-03-09
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    What makes you say 20 is not the right answer?2012-03-10

4 Answers 4