Discussion
If n(A) = 8, then the number of subsets of A which contain 2 or 6 elements is
Answer: D
The number of such subsets is 56.
A set of 8 elements has \(\binom{8}{r}\) subsets with exactly r elements. Subsets with 2 elements and subsets with 6 elements are disjoint groups, so add:
\[ \binom{8}{2} + \binom{8}{6} = 28 + 28 = 56 \]
The two counts are equal because choosing 2 elements to keep is the same as choosing 6 to leave out. 28 counts only one of the two groups. 216 does not come from a binomial coefficient of 8.
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