combinatorics
Permutations — AMC & AIME Problems
54 problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses 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.
LIVE focuses on challenge. As a social enterprise, we also explain standard school concepts one at a time, for free, on our sister site Expii. For this idea: What Is a Permutation?, What Is a Factorial?.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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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.
AMC 8
AMC 10
- 2002 AMC 10B Problem 9
- 2005 AMC 10B Problem 20
- 2007 AMC 10B Problem 20
- 2009 AMC 10B Problem 11
- 2011 AMC 10A Problem 22
- 2014 AMC 10A Problem 4
- 2017 AMC 10A Problem 25
- 2018 AMC 10A Problem 4
- 2018 AMC 10B Problem 18
- 2021 AMC 10B Spring Problem 22
- 2024 AMC 10A Problem 6
- 2024 AMC 10B Problem 17
- 2025 AMC 10B Problem 11
AMC 12
- 1976 AMC 12 Problem 30
- 1977 AMC 12 Problem 17
- 1985 AMC 12 Problem 11
- 1987 AMC 12 Problem 12
- 1987 AMC 12 Problem 27
- 1989 AMC 12 Problem 30
- 1991 AMC 12 Problem 26
- 2000 AMC 12 Problem 25
- 2001 AMC 12 Problem 16
- 2003 AMC 12B Problem 19
- 2008 AMC 12A Problem 21
- 2018 AMC 12A Problem 3
- 2019 AMC 12A Problem 16
- 2022 AMC 12A Problem 19
- 2025 AMC 12A Problem 18
AIME
- 1987 AIME Problem 13
- 1999 AIME Problem 13
- 2000 AIME I Problem 15
- 2000 AIME II Problem 5
- 2005 AIME II Problem 6
- 2007 AIME II Problem 1
- 2011 AIME II Problem 14
- 2014 AIME II Problem 13
- 2015 AIME II Problem 10
- 2016 AIME I Problem 8
- 2016 AIME II Problem 13
- 2017 AIME I Problem 11
- 2018 AIME II Problem 11
- 2020 AIME I Problem 5
- 2020 AIME II Problem 9
- 2021 AIME II Problem 3
- 2025 AIME I Problem 5
- 2026 AIME I Problem 7
More combinatorics concepts
- Arrangements with restrictions
- Basic counting
- Bijection
- Burnside’s Lemma
- Catalan Number
- Circular arrangements
- Combinations
- Combinatorial game
- Complementary counting
- Counting integers in a range
- Counting intersections
- Counting pairs
- Counting regions
- Counting shapes in figures
- Derangements
- Double counting
- Fencepost counting
- Generating functions
- Graph theory
- Inclusion-exclusion
- Lattice paths
- Multiplication principle
- Multiset permutations
- Partitions and compositions
- Pascal’s Triangle
- Pigeonhole principle
- Recursive counting
- Stars and bars
- Subsets
- Tiling
- Tree diagram
- Vandermonde’s Convolution
- Venn Diagram