Variation 3 · answer guide

Combinatorics — No three collinear case check

Question

If 5 points are in general position (no 3 collinear), equals

This practice question was inspired by Question 7 in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: count a simple unrestricted set first, then add or subtract the arrangements that break the condition., and none are collinear so all 10 form triangles.
Match the result to the choices and state the correct option.Therefore option A is correct.

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Bare combination count when no collinear exclusions apply.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.