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

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 · 2022 AMC 10A Problem 24

AMC 12

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

AIME

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