Combinatorics
Quant interviews often disguise counting problems as probability questions. The key skill is recognizing what is being counted and whether order matters.
Lessons · recommended order
- 1Permutations and CombinationsDistinguish ordered arrangements from unordered selections and count each correctly.Foundations7 min
- 2Multinomial CoefficientsCount the ways to partition a set into multiple labeled groups of specified sizes.Foundations7 min
- 3Stars and BarsCount the ways to distribute identical items into distinct groups, with or without lower bounds.Intermediate8 min
- 4Circular PermutationsCount arrangements around a circle and handle adjacency constraints with the block method.Intermediate6 min
- 5Inclusion-ExclusionCount the size of a union of overlapping sets by adding and subtracting intersections systematically.Intermediate8 min
- 6DerangementsCount permutations with no fixed points using inclusion-exclusion, and use the e^{-1} approximation.Intermediate7 min
- 7The Gap MethodCount selections or arrangements that forbid adjacency by placing items into the gaps between fixed elements.Intermediate6 min
- 8Lattice PathsCount monotonic grid paths using binomial coefficients, and recognize constrained-path (Catalan-style) variants.Intermediate7 min