Let $S = \{ 1, 2, \ldots, n \}$. The number of possible pairs of the form $(A, B)$ with $A \subseteq B$ for subsets $A$ and $B$ of $S$ is (A) $2^n$ (B) $3^n$ (C) $\sum _ { k = 0 } ^ { n } \binom { n } { k } \binom { n } { n - k }$ (D) $n!$
Let $S = \{ 1, 2, \ldots, n \}$. The number of possible pairs of the form $(A, B)$ with $A \subseteq B$ for subsets $A$ and $B$ of $S$ is\\
(A) $2^n$\\
(B) $3^n$\\
(C) $\sum _ { k = 0 } ^ { n } \binom { n } { k } \binom { n } { n - k }$\\
(D) $n!$