Combination Probability Interview Questions
Combination probability interview prep for unordered choices, hands, committees, subsets, exact counts, and hypergeometric-style prompts.
Candidates preparing for unordered samples and finite counting questions.
Order does not matter
Combinations count selections where order does not matter. Card hands, committees, subsets, and samples are common interview examples.
Use combinations for exact counts
If a hand needs exactly k successes, choose the successes and choose the remaining failures. Divide by all unordered samples of the same size.
Concrete example
The probability of exactly two aces in a five-card hand is C(4,2)C(48,3)/C(52,5). The order of cards in the hand is irrelevant.
At least one events
For at least one success, the complement can be cleaner: one minus the probability of zero successes. This avoids summing many exact-count cases.
Hypergeometric connection
Sampling without replacement and counting successes is hypergeometric. The formula is just combination counting with successes and failures.
Common mistakes
Candidates often mix ordered and unordered counts. If the denominator is C(52,5), the numerator should also count unordered hands.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.