Variation 1 · answer guide

Combinatorics — Select then rank

Question

From players, reach a final; then of those are ranked 1st–3rd. How many ways?

This practice question was inspired by Question 8 in the 2020 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.Choose : . Rank : .
Finish the calculation, then check that the result meets the question’s conditions.Product .
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: Numerical value .

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