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Multiset permutations — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Multiset permutations — a combinatorics concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

Filter by difficulty

These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.

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AMC 8

1994 AMC 8 Problem 8 • 2004 AMC 8 Problem 2 • 2009 AMC 8 Problem 16 • 2012 AMC 8 Problem 10

AMC 10

2008 AMC 10B Problem 22 • 2013 AMC 10A Problem 24 • 2019 AMC 10A Problem 17 • 2020 AMC 10B Problem 5

AMC 12

1985 AMC 12 Problem 11 • 2003 AMC 12A Problem 20 • 2012 AMC 12A Problem 11 • 2021 AMC 12A Fall Problem 18 • 2024 AMC 12A Problem 16

AIME

1990 AIME Problem 8 • 2001 AIME II Problem 11 • 2008 AIME I Problem 9 • 2009 AIME I Problem 9 • 2018 AIME II Problem 8 • 2018 AIME II Problem 15 • 2019 AIME I Problem 5 • 2022 AIME I Problem 9 • 2023 AIME II Problem 10 • 2025 AIME I Problem 3

More combinatorics concepts

arrangements with restrictionsbasic countingbijectionBurnside’s LemmaCatalan Numbercircular arrangementscombinationscombinatorial gamecomplementary countingcounting integers in a rangecounting intersectionscounting pairscounting regionscounting shapes in figuresderangementsdouble countingfencepost countinggenerating functionsgraph theoryinclusion-exclusionlattice pathsmultiplication principlepartitions and compositionsPascal’s Trianglepermutationspigeonhole principlerecursive countingstars and barssubsetstilingtree diagramVandermonde’s ConvolutionVenn Diagram