AMC counting & probability problems

Counting techniques, permutations and combinations, and probability — including expected value and recursion.

576 problems in the archive use these ideas — 314 from the AMC 10 and 262 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

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Basic Counting172
Systematic listing, the multiplication principle and counting integers in a range.
Permutations & Combinations168
Arrangements, combinations, factorials, subsets, and stars and bars.
Counting Techniques141
Complementary counting, inclusion-exclusion, bijections, recursion and the pigeonhole principle.
Probability213
Basic and conditional probability, independent events, geometric probability and expected value.

60 most recent problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

Use Start counting & probability practice above to keep going through the remaining 516, or browse them by contest in the AMC 12 and AMC 10 archives.