75 Given the set $A=\{1.2,3.4,5,6\}$. For $X \subseteq A$, define $S(X)$ as the sum of all elements in $X$, then the total sum of all $S(X)$ is $S=$ $\qquad$ .
75 672. The subsets of $A$ can be paired into $(X, Y)$ such that $X \cup Y=A$, and $X \cap Y=\emptyset$. It is easy to see that
$$
S(X)+S(Y)=S(A)=21,
$$

and $A$ has $2^{6}$ subsets, which can be paired into $2^{5}$ pairs, so
$$
S=21 \times 2^{5}=672
$$