Combinatorics — One triple only

Question

Find the number of distinct arrangements of the letters in BANANA.

This practice question was inspired by Question 11(b) 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.

Set up the solution: count a simple unrestricted set first, then add or subtract the arrangements that break the condition. letters: A , N , B .
State the final answer clearly in the form the question requested.Count .

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.