For $k = 1 , \ldots , n$, let $F ( n , k )$ be the number of good lists of length $n$ which result in team $n$ booking room $k$. Explain why $F ( n , k )$ is a multiple of $k$.
For $k = 1 , \ldots , n$, let $F ( n , k )$ be the number of good lists of length $n$ which result in team $n$ booking room $k$.
Explain why $F ( n , k )$ is a multiple of $k$.