Combinations — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Combinations — 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.
AMC 8
1996 AMC 8 Problem 21 • 2001 AMC 8 Problem 14 • 2002 AMC 8 Problem 21 • 2004 AMC 8 Problem 4 • 2005 AMC 8 Problem 21 • 2006 AMC 8 Problem 20 • 2012 AMC 8 Problem 14 • 2014 AMC 8 Problem 18 • 2017 AMC 8 Problem 10 • 2020 AMC 8 Problem 7 • 2025 AMC 8 Problem 25 • 2026 AMC 8 Problem 20
AMC 10
2001 AMC 10 Problem 19 • 2004 AMC 10A Problem 5 • 2005 AMC 10A Problem 9 • 2005 AMC 10B Problem 15 • 2005 AMC 10B Problem 18 • 2005 AMC 10B Problem 21 • 2007 AMC 10B Problem 8 • 2007 AMC 10B Problem 20 • 2008 AMC 10A Problem 23 • 2009 AMC 10A Problem 24 • 2010 AMC 10A Problem 22 • 2011 AMC 10A Problem 21 • 2013 AMC 10A Problem 7 • 2013 AMC 10A Problem 11 • 2013 AMC 10A Problem 25 • 2016 AMC 10A Problem 20 • 2016 AMC 10B Problem 22 • 2017 AMC 10A Problem 8 • 2017 AMC 10B Problem 18 • 2019 AMC 10B Problem 25 • 2020 AMC 10B Problem 11 • 2020 AMC 10B Problem 18 • 2020 AMC 10B Problem 19 • 2020 AMC 10B Problem 25 • 2021 AMC 10A Spring Problem 15 • 2021 AMC 10A Fall Problem 13 • 2021 AMC 10A Fall Problem 21 • 2022 AMC 10A Problem 22 • 2023 AMC 10A Problem 16 • 2024 AMC 10A Problem 9 • 2024 AMC 10B Problem 12 • 2024 AMC 10B Problem 17 • 2024 AMC 10B Problem 22 • 2025 AMC 10A Problem 24
AMC 12
1950 AMC 12 Problem 45 • 1952 AMC 12 Problem 31 • 1958 AMC 12 Problem 49 • 1959 AMC 12 Problem 50 • 1976 AMC 12 Problem 23 • 1976 AMC 12 Problem 28 • 1980 AMC 12 Problem 20 • 1982 AMC 12 Problem 8 • 1984 AMC 12 Problem 19 • 1989 AMC 12 Problem 9 • 1989 AMC 12 Problem 22 • 1990 AMC 12 Problem 16 • 1990 AMC 12 Problem 17 • 1993 AMC 12 Problem 24 • 1993 AMC 12 Problem 28 • 1996 AMC 12 Problem 10 • 1996 AMC 12 Problem 26 • 1997 AMC 12 Problem 24 • 1997 AMC 12 Problem 30 • 1999 AMC 12 Problem 24 • 2003 AMC 12A Problem 20 • 2004 AMC 12A Problem 13 • 2005 AMC 12B Problem 11 • 2006 AMC 12A Problem 25 • 2006 AMC 12B Problem 9 • 2008 AMC 12B Problem 22 • 2010 AMC 12A Problem 18 • 2012 AMC 12B Problem 12 • 2012 AMC 12B Problem 18 • 2013 AMC 12B Problem 21 • 2014 AMC 12A Problem 13 • 2014 AMC 12B Problem 23 • 2016 AMC 12B Problem 20 • 2019 AMC 12B Problem 23 • 2020 AMC 12B Problem 16 • 2021 AMC 12A Spring Problem 15 • 2021 AMC 12A Fall Problem 22 • 2023 AMC 12A Problem 13 • 2023 AMC 12B Problem 8 • 2025 AMC 12A Problem 13
AIME
1983 AIME Problem 7 • 1984 AIME Problem 11 • 1986 AIME Problem 11 • 1988 AIME Problem 1 • 1988 AIME Problem 10 • 1989 AIME Problem 2 • 1990 AIME Problem 8 • 1992 AIME Problem 2 • 1992 AIME Problem 4 • 1992 AIME Problem 12 • 1996 AIME Problem 7 • 1997 AIME Problem 2 • 1998 AIME Problem 4 • 1999 AIME Problem 10 • 2000 AIME II Problem 3 • 2000 AIME II Problem 5 • 2003 AIME I Problem 13 • 2004 AIME II Problem 2 • 2005 AIME I Problem 3 • 2005 AIME I Problem 5 • 2005 AIME II Problem 1 • 2006 AIME II Problem 4 • 2006 AIME II Problem 8 • 2006 AIME II Problem 10 • 2007 AIME I Problem 10 • 2008 AIME II Problem 12 • 2010 AIME II Problem 8 • 2010 AIME II Problem 13 • 2011 AIME II Problem 6 • 2012 AIME I Problem 5 • 2012 AIME II Problem 3 • 2012 AIME II Problem 7 • 2013 AIME I Problem 4 • 2013 AIME I Problem 6 • 2013 AIME II Problem 11 • 2015 AIME I Problem 2 • 2015 AIME I Problem 12 • 2017 AIME I Problem 1 • 2017 AIME I Problem 7 • 2017 AIME II Problem 9 • 2018 AIME I Problem 10 • 2018 AIME I Problem 12 • 2018 AIME II Problem 10 • 2020 AIME I Problem 7 • 2022 AIME I Problem 12 • 2022 AIME II Problem 10 • 2023 AIME I Problem 1 • 2023 AIME I Problem 3 • 2023 AIME I Problem 14 • 2024 AIME I Problem 4 • 2025 AIME II Problem 10 • 2026 AIME II Problem 5