Question 17
Find the number of ordered pairs $(A, B)$ such that the following conditions hold:
- $A$ and $B$ are disjoint subsets of $\{1,2, \ldots, 50\}$.
- $|A|=|B|=25$
- The median of $B$ is 1 more than the median of $A$.
- $A$ and $B$ are disjoint subsets of $\{1,2, \ldots, 50\}$.
- $|A|=|B|=25$
- The median of $B$ is 1 more than the median of $A$.