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← 2023 HSC Extension 1 paper Question 12(d)

Variation 1 · answer guide

Combinatorics — Small Pascal merge

Question

Find such that .

This practice question was inspired by Question 12(d) in the 2023 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: count a simple unrestricted set first, then add or subtract the arrangements that break the condition..
  2. State the final answer clearly in the form the question requested.So , (or ).

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

Verification: Direct Pascal identity.

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

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