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Question 2

Five friends A, B, C, D, and E go on a trip together. Each of them likes at least one of the following three activities: Countryside Sightseeing, Shopping, and Adventure Sports such that:

  • No two friends like exactly the same set of activities.
  • A, B and E like exactly two activities each.
  • D likes only Countryside Sightseeing.
  • C likes more number of activities compared to D.

The number of friends that like Countryside Sightseeing is ____


Correct Answer: 4

Each friend likes a non-empty subset of {Countryside (Co), Shopping (Sh), Adventure (Ad)} — 7 possible subsets in all.

  • D likes only {Co}.
  • A, B, E each like exactly 2 activities; with three distinct 2-element subsets available ({Co,Sh}, {Co,Ad}, {Sh,Ad}) and all three friends needing distinct sets, they cover all three pairs.
  • C must like more than D (more than 1) and a set different from A/B/E. The only remaining option is the full 3-set {Co, Sh, Ad}.

Who likes Countryside? D (only Co), C (all three), and the two of A/B/E whose 2-element subset contains Co (namely {Co,Sh} and {Co,Ad}). The third A/B/E (with {Sh,Ad}) does not. Total = 4.

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