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Sampling without replacement — AMC & AIME Problems

Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Sampling without replacement — a probability and statistics 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

1986 AMC 8 Problem 24 • 2007 AMC 8 Problem 21

AMC 10

2001 AMC 10 Problem 23 • 2005 AMC 10B Problem 21 • 2013 AMC 10B Problem 12 • 2016 AMC 10A Problem 12 • 2018 AMC 10B Problem 6

AMC 12

1980 AMC 12 Problem 20 • 1984 AMC 12 Problem 19 • 2001 AMC 12 Problem 11 • 2021 AMC 12B Fall Problem 23

AIME

1990 AIME Problem 6 • 1991 AIME Problem 13 • 1993 AIME Problem 7 • 1994 AIME Problem 9 • 2004 AIME II Problem 2 • 2005 AIME II Problem 2 • 2015 AIME I Problem 5 • 2026 AIME II Problem 5

More probability and statistics concepts

basic probabilityBayes’ Theorembinomial probabilitycomplementary probabilityconditional probabilitydata and graph interpretationdice (probability)expected valuegeometric distributiongeometric probabilityharmonic meanindependent eventsmeanmedian (data)moderandom walkrangerecursive probabilitysampling with replacementweighted mean