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2020 PUMaC Combinatorics A4 / B5

Source:

January 1, 2022

combinatorics

Problem Statement

Let

P

be the power set of

\{1, 2, 3, 4\}

(meaning the elements of P are the subsets of

\{1, 2, 3, 4\}

). How many subsets

S

of

P

are there such that no two distinct integers

a, b \in \{1, 2, 3, 4\}

appear together in exactly one element of

S

?

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