Question 12

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 ways in which a pair of friends can be chosen for a trip from those who like Adventure Sports is ____

Correct Answer: 3

From the same setup: A/B/E cover {Co,Sh}, {Co,Ad}, {Sh,Ad}; C likes all three; D likes only {Co}.

Who likes Adventure? The two of A/B/E whose 2-set contains Ad (i.e., {Co,Ad} and {Sh,Ad}), plus C. Total = 3 friends.

Number of pairs of friends from these 3 = $$\binom{3}{2} = \mathbf{3}$$.

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