A historian is organizing 4 rare manuscripts into 3 indistinguishable role-based archives: Royal, Scholarly, and Commercial. Each manuscript must be assigned to exactly one archive. How many distinct ways can the manuscripts be assigned, considering only the number per archive matters?

Wed, 06 May 2026 09:39:43 +0000

Title: How Many Ways Can a Historian Assign 4 Rare Manuscripts to 3 Indistinguishable Archives? Organizing rare historical manuscripts into specialized collections requires careful organization—especially when inventory is limited and preservation, context, and role define how items are grouped. This article explores a classic partitioning problem: assigning 4 rare manuscripts into 3 indistinguishable archives, where each manuscript must be placed in exactly one archive and only the count per archive matters. ### Understanding the Problem A historian is organizing 4 distinct historical manuscripts into 3 indistinguishable role-based archives labeled Royal, Scholarly, and Commercial. However, unlike labeled containers, these archives serve such similar functional roles that their order is irrelevant—meaning assigning manuscripts A to Royal, B to Scholarly, and C to Commercial is equally valid as assigning them the same alongside different labels.