The question is the following: how many subsets of size $5$ from a set $A$ of size $16$ do we need so that any subset of size 2 of $A$ is also a subset of one of the selected subsets of size $5$?
How does this the required number change as we change 16 to another number and if we change $5$ to another number? Perhaps an even harder question is if we change $2$ to another number.