This is a counting question, which used to appear on the old SAT (pre-2016) but don’t appear on the current SAT. I just wanted to point that out before getting into it because I didn’t want to scare anyone. I assume you’re prepping for a Subject Test (or maybe even GRE or something like that).

My advice is to draw the points, draw the segment, and count AS YOU DRAW (not after you draw). Start with a point, draw every segment that can be drawn from that point to another point. When you’ve drawn every segment you can from that one point, go to the next one. Like so:

 

You know you’re done when you’ve got a nice enclosed star design like above. You drew 5 + 4 + 3 + 2 + 1 = 15 segments.

From where I sit, I really think that if you care about always getting questions like this right on whatever standardized test you’re prepping for, you should practice doing it by drawing and counting like I did above.

However, you can also solve this with combinations. Each segment connects two points. How many combinations of two items can you choose from a list of six items? If you know nCr notation, 6C2 = 15. If you don’t, well, you’ve always got factorials…

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