Question: 2014 Winter Final - 8

Consider a group of $n$ people, let $k$ be an integer with $1 \leq k \leq n$, and consider a circular table with $k$ chairs around it. We select $k$ people and seat them around this table. How many different seating arrangements are there? (Two seating arrangements $A$ and $B$ are the same if for each person, the clockwise neighbor in $A$ is the same as the clockwise neighbor in $B$, and the counterclockwise neighbor in $A$ is the same as the counterclockwise neighbor in $B$.)