Let S be a set of 5 elements and P ( S ) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the set P(S) × P(S)…

Let S be a set of $\displaystyle 5$ elements and $\displaystyle \mathrm{P}(\mathrm{S})$ denote the power set of S . Let E be an event of choosing an ordered pair $\displaystyle (A, B)$ from the set $\displaystyle P(S) \times P(S)$ such that $\displaystyle A \cap B=\emptyset$. If the probability of the event E is $\displaystyle \frac{3^{\mathrm{p}}}{2^{\mathrm{q}}}$, where $\displaystyle \mathrm{p}, \mathrm{q} \in \mathrm{N}$, then $\displaystyle \mathrm{p}+\mathrm{q}$ is equal to $\displaystyle \_\_\_\_$