Question 10
Let $S$ be a set with six elements. Let $P$ be the set of all subsets of $S.$ Subsets $A$ and $B$ of $S,$ not necessarily distinct, are chosen independently and at random from $P.$ The probability that $B$ is contained in at least one of $A$ or $S - A$ is $\frac{m}{n^r},$ where $m,$ $n,$ and $r$ are positive integers, $n$ is prime, and $m$ and $n$ are relatively prime. Find $m + n + r.$ (The set $S - A$ is the set of all elements of $S$ which are not in $A.$)