Logo

Question preview

Delicious donuts

What this preview is

About this preview

Delicious donuts is a easy quant interview question on probability.

Unlock full access to getcracked

Join to unlock this question, detailed solutions, and our complete library of quant finance interview prep.

What this combinatorics interview question tests

This is an easy combinatorics problem that appears in probability and statistics interview rounds. It asks you to count the number of ways to distribute indistinguishable items (donuts) into distinguishable categories (types) subject to a constraint (at least one of each type).

The core skill is recognizing when a problem is asking for compositions with constraints rather than raw permutations. Since order doesn't matter—only the final count of each type in the box—you need to think in terms of how many donuts of each type to include. The constraint that every type must be represented rules out many naive distributions and forces you to account for that systematically.

  • Stars and bars (distributing indistinguishable objects into distinguishable bins)
  • Constraint-handling via change of variables
  • The difference between ordered and unordered selections