Let S be a set containing n distinct objects. Verify that ex/(I - x)k is the exponential

Question:

Let S be a set containing n distinct objects. Verify that ex/(I - x)k is the exponential generating function for the number of ways to choose m of the objects in S, for 0 < m < ft, and distribute these objects among k distinct containers, with the order of the objects in any container relevant for the distribution.