Question: A science fair judge ranks 5 student projects from best to worst, but two projects, A and B, are tied for rank 3. The judge randomly assigns the actual ranks under the constraint that no two projects are tied — meaning ties are broken, but in this case, the rule implies that the rank distribution must reflect the observed ties. However, the judge decides that exactly one tie occurs, and it must be between A and B. How many distinct ranking configurations (i.e., total orderings with ties) satisfy this?

Tue, 05 May 2026 19:20:22 +0000

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