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The power set contains every subset, including the empty set and the whole set. Each element is either in or out of a given subset, so there are 2ⁿ subsets in total.
Power set size
|P(A)| = 2^|A|
Subsets of size k
C(n, k)
2³ = 8, of which C(3,2) = 3 have exactly two elements.
Yes, vacuously — there is no element of it that fails to be in the other set.