Selection of pairs with balanced number items across selections

Dear all,

I'm looking for a solution to 'n choose k' problem, but one in which you don't need ALL combinations and can limit the number of times each item gets selected.

For example, let's say we have a set of 10 numbers from 0 to 9 and you wish to get pairs of these numbers. However, you only want to obtain as many pairs to get each number to show only 3 times across all the pairs. Results from '10 choose 2' will give you each number 9 times across all pairs.

Is there a way to do this?

I'd appreciate your help, thanks!