Count Cookie Flavor Combinations
Company: Sig
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Online Assessment
# Count Cookie Flavor Combinations
You will bake exactly 5 cookies using 4 available flavors. A flavor may be used for any number of cookies, including zero, and the order of the cookies does not matter.
How many distinct flavor-count combinations are possible? Show a counting argument rather than listing all combinations.
### What a Strong Answer Covers
- Translation into nonnegative integer solutions of a four-variable sum.
- Correct use of combinations with repetition or stars and bars.
- A distinction between count combinations and ordered flavor sequences.
- Evaluation of the final binomial coefficient.
### Follow-up Questions
- How many combinations use every flavor at least once?
- How would the count change if no flavor could appear more than twice?
Overview: Count ways to make five cookies from four reusable flavors when only flavor totals matter. The solution translates the task into nonnegative integer solutions, applies stars and bars, derives 56 combinations, and contrasts this with the much larger ordered-sequence count.
Read the full Sig Data Scientist interview experience this question came from