Combinatorics — Two repeated letters

Question

How many distinct linear arrangements of the letters in MISSISSIPPI are there?

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: I , S , P , M .
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: Divide by each repeated-letter factorial.

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