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Not sure why you subtracted ABC,AED,BCD,BAE..etc. I interpreted the question stem as "maximum" possible triangles that can be formed by the points, A, B, C, D, E and F. We know they are all non-collinear. So, you can choose any three points and form a triangle.

thats correct. In such questions very important to note whether points are collinear or not.
Praet, try to solve this and u will know when to subtract sides:
How many triangles can be formed by connecting vertices of a hexagon such that no side of triangle coincides with that of hexagon.

Not sure why you subtracted ABC,AED,BCD,BAE..etc. I interpreted the question stem as "maximum" possible triangles that can be formed by the points, A, B, C, D, E and F. We know they are all non-collinear. So, you can choose any three points and form a triangle.

Hope this helps.

absolutely agree. the paints are not collinear and the question does not asks to count different triangles, so its solution should be simple 3C6=20.

Chose a point and then chose 2 out of 5 remaining points
so we have 5C2 per point. For 6 points we have
6 * 5C2 triangles.
Since triangle ABC is same as BCA and CAB we need to divide the combinations by 3
so total triangles = 6 * 5C2 /3 = 20