In this problem, if we are choosing 3 vertices out of 7 (7C3), shouldn’t we subtract 7 from it since we don’t want 3 vertices that are in the same straight line?

Please help me in understanding what I’m missing.

In this problem, if we are choosing 3 vertices out of 7 (7C3), shouldn’t we subtract 7 from it since we don’t want 3 vertices that are in the same straight line?

Please help me in understanding what I’m missing.

I don’t think that can happen, since there is no triplet of points that are on a line.

I understand what you’re saying but I meant 3 points in one order. For eg, what if A B C are chosen? That doesn’t give us a triangle right

I don’t see why it wouldn’t - just draw AB, BC and AC in the above figure.

Oh right right. I wasn’t seeing it this way all this time. My bad. You’re correct. It should be 7C3 only then, no constraints. Thank you so much for your response!