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

D likes only Countryside Sightseeing, so D's set has $1$ activity. C must like more, so C likes $2$ or $3$ activities.

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A, B and E each like exactly $2$ activities. The only $2$ activity options are $\{\text{CS}, \text{Sh}\}$, $\{\text{CS}, \text{AS}\}$ and $\{\text{Sh}, \text{AS}\}$. Since no two friends share a set, A, B and E together take all three options in some order.

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C cannot take another $2$ activity set without repeating one, so C likes all three.

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The filled table:

Friend	CS	Sh	AS
D	$\checkmark$	$-$	$-$
One of A/B/E	$\checkmark$	$\checkmark$	$-$
One of A/B/E	$\checkmark$	$-$	$\checkmark$
One of A/B/E	$-$	$\checkmark$	$\checkmark$
C	$\checkmark$	$\checkmark$	$\checkmark$

From the table, look at the AS column and count the rows that show $\checkmark$.

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These are the second A/B/E row, the third A/B/E row, and C. So $3$ friends like Adventure Sports.

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Number of pairs from these $3$ friends:

${}^{3}C_{2} = \dfrac{3 \times 2}{2 \times 1} = 3$