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How many distinct triangles can be formed by selecting three vertices of a regular hexagon? (Triangles with different vertices are considered distinct even if they are congruent.)

 Jun 13, 2021
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A regular hexagon has 6 vertices.   Any subset of 3 vertices of the hexagon forms a triangle.   So you have to count the number of subsets of size-3 of a set of size 6.    Or you can think of it as the number of ways to choose 3 objects out of 6 distinct objects, where order doesn't matter.   E.g., if you choose 1, 2, then 3,  it's considered the same way as choosing vertex 2, 1, then 3.   Either way you get the triangle 123.
 

 Jun 13, 2021

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