We have 20 objects, 10 of which are dice and 10 of which are balls - and we can distinguish them all - and we have two baskets; and in each basket we throw 10 objects. Can someone please explain to me how to calculate the number of possibilities of obtaining two baskets that contain the same amount of equals objects ?
In the solution to this problem, only "$\frac{10!}{(5!)^2} \cdot \frac{10!}{(5!)^2} $" was specified.
Would it make any difference, if we couldn't distinguish the objects ?