Question 5
Let $n$ be a natural number. A volleyball team consisting of $n$ women and $n$ men lines up for a game. Each team member occupies one of the positions $1,2, \ldots, 2 n$, where exactly the positions $1$ and $n+1$ are outside the court. During the game all team members rotate, each moving from position $i$ to position $i+1$ (respectively from $2 n$ to $1$). How many possibilities are there for the starting line-up such that there are always at least $n-1$ women on the court, no matter how often the team rotates?
Remark: Two starting line-ups are different if at least one team member occupies a different position.
Remark: Two starting line-ups are different if at least one team member occupies a different position.