Math CentralQuandaries & Queries


Question from deciree, a student:

Given 12 points, no 3 of them on a line with 6 red, 4 blue and 2 green points.
a)How many triangles have vertices all the same color?
b)How many triangles have vertices with each vertex a different color?
c)How many triangles have at least one green vertex?

thanks to lorraine!


I can help get you started on a).

How many triangles have all green vertices?

The answer is clearly none since it takes three vertices to make a triangles.

How many triangles have all blue vertices?

There are 4 blue vertices and it takes 3 to form a triangle so the number of triangles with blue vertices is the number of ways of choosing 3 vertices from 4. That is 4 choose 3 which is 4.

How many triangles have all red vertices?

Now it's your turn.


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