Do you mean ?
I am not sure about this. I think it is the number of ways of selecting -object subsets from elements. I.e., when we are taking about combinations , usually ; when . When we are talking about combinations with repetitions , which is the number of ways to put objects into bins, may be greater than .I know that (n choose k) represents putting k identical objects into n bins.
This Wikipedia page lists the following property:
which is equivalent to what you need to prove. It suggests proving it by induction on using the Pascal's rule.