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HMMT 2022 C1

  • Combinatorics
  • Answer

Sets A,BA, B, and CC satisfy ∣A∣=92,∣B∣=35,∣C∣=63,∣A∩B∣=16,∣A∩C∣=51,∣B∩C∣=19|A|=92,|B|=35,|C|=63,|A \cap B|=16,|A \cap C|=51,|B \cap C|=19. Compute the number of possible values of ∣A∩B∩C∣|A \cap B \cap C|.

Dataset text NuminaMath olympiads. Quoted with source.

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