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← 2020 HSC Extension 1 paper Question 8

Variation 3 · answer guide

Combinatorics — Different finalist count

Question

From contestants, are chosen for a final and all are then fully ranked. How many ways?

  4. is different from

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.

Step by step

  1. Set up the solution: count a simple unrestricted set first, then add or subtract the arrangements that break the condition.Choose then rank all : .
  2. Finish the calculation, then check that the result meets the question’s conditions.So the count is .
  3. 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: .

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

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