Consider the case where we have a bag of 'N' unique marbles, and we randomly select all 'S' possible sets of size 'm' from the bag (with replacement) under the following constraints:
(1) - Any set of 'm' marbles must have all unique elements, i.e. there must be no duplicate copies of a marble in any given set.
(2) - The maximum intersection between any two sets, i.e. the number of unique marbles they have in common, can be of at most size 'k'.
Provided (1) & (2), what is 'S'? Equivalently, what is the number of possible sets of size 'm' obeying the aforementioned constraints?