Variation 2 · answer guide

Combinatorics — With replacement contrast

Question

If the first coin is replaced, becomes

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.Independence: and .
Finish the calculation, then check that the result meets the question’s conditions.Sum is option A.
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: This is the distractor D from the original paper.

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