Combinatorics — Positive linear term

Question

Coefficients of and in .

This practice question was inspired by Question 11(c) 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.: .
State the final answer clearly in the form the question requested.: .

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

Verification: Same magnitudes as the original; coefficient is now positive.

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