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CHMMC 2022 Winter / 2022-23 Team #6

Source:

August 10, 2023
combinatoricsnumber theory

Problem Statement

Let AA be a set of 88 elements, and B:=(B1,...,B7)B := (B_1,...,B_7) be an ordered 77-tuple of subsets of AA. Let NN be the number of such 77-tuples BB such that there exists a unique 44-element subset I⊆{1,2,...,7}I \subseteq \{1,2,...,7\} for which the intersection ∩i∈IBi\cap _{ i\in I} B_i is nonempty. Find the remainder when NN is divided by 6767.
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