Combinatorics quant interview questions

Combinatorics interview questions test whether you can count carefully and spot structure before brute force. In quant trading and research interviews you will meet arrangements with restrictions, committees and seating problems, stars and bars, inclusion–exclusion, derangements, lattice paths and pigeonhole arguments. Good answers come from choosing a clean bijection or complementary count, then sanity-checking with a small case. Many probability questions reduce to a counting problem, so fluency here pays off across the whole interview. This collection moves from standard counting identities to harder problems that combine several techniques, with hints and worked solutions on every free problem. Use the list to drill a specific subtopic, or practise interactively to track your accuracy and see which counting methods still slow you down.