Solution: This is equivalent to finding the number of ways to partition 6 distinguishable objects into 4 non-empty, indistinct subsets. This corresponds to the Stirling number of the second kind, $ S(6,4) $. The value of $ S(6,4) $ is calculated as follows:

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**Discover: Unlocking Mathematical Foundations in Everyday Choices**
How does organizing complexity reveal patterns behind what we don’t see? A lesser-known mathematical concept offers clarity: the Stirling number of the second kind, $ S(6,4) $. This number represents the ways to divide six distinct items into four non-empty, indistinct groups—a concept with broader implications for understanding structured systems, from resource allocation to personalized learning. For readers exploring logistics, curriculum planning, or strategic resource division, $ S(6,4) $ offers more than a formula. It illustrates how complex groupings emerge from simple rules—an insight increasingly relevant in a world where precision and intentionality guide decision-making. This approach supports clearer planning in domains like education, operations, and data partitioning. **Why This Problem Matters in the US Context**
In today’s data-driven environment, the ability to categorize and structure diverse sets—whether classes into heterogeneous groups, customers into tiered segmentation patterns, or tasks into reliable workflows—delivers tangible value. Meeting rising expectations for personalized, effective systems relies on robust underlying logic. Understanding $ S(6,4) $ grounds users in how complex sets can be meaningfully partitioned, revealing how small changes in grouping influence outcomes. At 6 objects, dividing into 4 non-empty subsets produces exactly 65 distinct arrangements. This number isn’t just academic—it reflects real-world scenarios where dividing diversity into inclusive, balanced subsets enhances fairness, efficiency, and insight.