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What this combinatorics interview question tests

This is an easy combinatorics problem that appears often in quant interview rounds. It tests whether you can recognize and apply the "stars and bars" technique—a foundational method for counting distributions of indistinguishable objects into distinguishable categories. The problem is small enough to solve by hand, but the real skill is identifying the right formula rather than brute-force enumeration.

Interviewers ask questions like this to confirm you have solid combinatorial intuition and can map a real-world constraint (identical cookies, different flavors) onto the appropriate counting model. The approach generalizes directly to problems involving portfolio allocations, inventory distributions, and sampling with replacement.

• Compositions and partitions
• Multiset counting
• The relationship between repetition and symmetry in counting problems