Let $B$ be a finite Boolean algebra of cardinality 64. Let $x \in B$ be an element represented as the join (supremum) of exactly 3 distinct atoms of $B$, and let $y \in B$ be an element represented as the join of exactly 4 distinct atoms of $B$. How many pairs $(x, y)$ satisfy $x \land y = 0$, where $0$ is the bottom element of the Boolean algebra?