How many ways can the manager of a baseball team put together a batting order of his nine players, if the shortstop must bat 3rd?

Answer 1

If the shortstop must bat 3rd, we can fix the shortstop in the 3rd position. The rest of the players can be arranged in the remaining 8 positions in $(8-1)! = \boxed{7! = 5,\!040}$ ways.