There are $8$ pairs of $2$ balls, for a total of $16$ balls each. Two balls in the same pair are indistinguishable, but distinguishable from other pairs. How many ways are there to put these balls into $3$ bins where order doesn't matter?
I know that the "Stars and Bars" strategy is to put $n$ indistinguishable objects into $k$ distinguishable bins, but here, some balls are distinguishable and some balls are indistinguishable. I haven't made much progress on the problem. I know how to solve this problem if the balls were all distinguishable and evenly fit into the three bins. However, this problem seems to be a lot trickier. May I have some help? Thanks in advance.