Counting & Probability on the AMC 10
216 of the 1,300 problems since 2000 (16.6%) have their main idea in this category, spread across 11 topics.
Topics in Counting & Probability
- Arrangements with Restrictions25
Permutations with constraints, adjacency, circular arrangements, forbidden positions
- Basic Counting57
Multiplication principle, permutations, combinations, counting by listing
- Basic Probability56
Sample-space probability: dice, coins, cards, random selection
- Conditional Probability & States17
Conditional probability, states/Markov-style processes, sequential random events
- Distributions & Stars and Bars5
Distributing objects into bins, integer partitions, compositions
- Expected Value5
Expected value, linearity of expectation, fair games
- Games & Processes14
Turn-based games, iterated processes, tournaments, scheduling
- Geometric Probability16
Probability as a ratio of lengths, areas, or volumes
- Inclusion-Exclusion6
Overlapping sets, Venn diagrams, PIE counting
- Paths & Grids12
Lattice paths, grid walks, board colorings and configurations
- Recursive Counting3
Counting via recurrences: tilings, Fibonacci-type, strings with no forbidden patterns