Question 32
Find the number of subsets $S$ of $\{1,2, \ldots, 48\}$ satisfying both of the following properties:
- For each integer $1 \leq k \leq 24$, exactly one of $2k-1$ and $2k$ is in $S$.
- There are exactly nine integers $1 \leq m \leq 47$ so that both $m$ and $m+1$ are in $S$.
- For each integer $1 \leq k \leq 24$, exactly one of $2k-1$ and $2k$ is in $S$.
- There are exactly nine integers $1 \leq m \leq 47$ so that both $m$ and $m+1$ are in $S$.