Variation 1 · answer guide

Combinatorics — Unordered equivalent

Question

For the same bag, the same-metal probability as an unordered selection of coins is

This practice question was inspired by Question 9 in the 2024 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.Favourable unordered pairs: both silver or both bronze.
Finish the calculation, then check that the result meets the question’s conditions.Divide by . This equals the ordered form A of the original.
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: Algebra: .

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