Selection over combinatorics that satisfies a distribution
Consider the following special case where for each element $i$ the table contains the constraint $\#i \geq (1/l) \cdot l$. This means we need to select the sets in such a way that each element appears at least once. This problem is called the set covering problem, where you have to output whether there is a subset of $l$ sets in the input that covers all the elements in the ground-set. It is an NP-complete problem and since it is a special case of your problem, your problem is NP-complete as well (it is clearly in NP since an NTM can guess all possible tuples of $l$ subsets and accept if the union of subsets in any of the guessed tuples covers the ground-set). So You should not expect a polynomial answer.

On the other hand, an exponential trivial solution would be to try packing all sets of $l$ subsets which are at most $n \choose l$ and try for each of them if they satisfy all the constraints in $O(l \cdot r)$ where $r$ is the number of the constraints. This totals in an $O(n^{l+1}r)$. There are a lot of improvements on this running time I think but you should not expect something sub-exponential.