Inverted Combinatorics Function

So I made up the words in that title...but, I am unsure if such a function exists. Let me formulate the question (I also have this on Quora):

Is there such a function in combinatorics that given a single value 0 to totalCombinations-1 it can return a unique set of subsets in the total combinatoric space. For Example: say we have a set S=A,B,C,D and we want to choose 2, thus total combinations = 6 (nCr(4,2))
I would like a function something like f(0) = A,B; f(1) = A,C; f(2) = A,D....f(6) = C,D


Does this function exist and at scale for magnitudes of combinations? So for any n f(n) = Item1, Item2...ItemN
Forgive my ignorance.

What you are referring to is called a combinadic. See my post here for how to apply it to a 7-card poker hand (52 choose 7). You can adjust the code to fit your needs.

Also, the original source where I found this information can be found here.

You have made my month. 1000 Thanks.

For additional information:

http://en.wikipedia.org/wiki/Combinatorial_number_system