MathNet 2007-part-01 — 187 problems (EN–VI) Question 156

Let $T = \{1, 2, 3, 4, 5, 6, 7, 8\}$. Find the number of all nonempty subsets $A$ of $T$ such that $3|S(A)$ and $5 \nmid S(A)$, where $S(A)$ is the sum of all elements of $A$.