Counting Methods for Quant Interviews
How to choose combinations, permutations, complements, inclusion-exclusion, and symmetry in quant interview counting problems.
Candidates who overcount or undercount probability and combinatorics interview questions.
Ask whether order matters
The first counting question is order. If order matters, permutations or sequences may fit. If order does not matter, combinations may fit. Do not start multiplying until this is clear.
Ask whether repetition is allowed
Replacement and repetition change the count. Rolling dice allows repeated values. Drawing cards without replacement does not. Password-style prompts may allow repeated characters unless the prompt says otherwise.
Use complements for broad events
At least one, no more than, and collision events are often easier by complement. Count the clean opposite case and subtract from the total or from one.
Concrete example
The number of five-card hands with exactly two aces is C(4,2)C(48,3). Order does not matter because a hand is unordered. If the prompt were ordered draws, the counting expression would change.
Use inclusion-exclusion for overlap
When cases overlap, simple addition double-counts. Inclusion-exclusion adds individual counts, subtracts intersections, and continues as needed. Use it only after naming the overlapping events clearly.
Common mistakes
Candidates often divide by a symmetry factor they cannot explain, or mix ordered favorable counts with unordered totals. Every count should answer: what object am I counting exactly once?
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.