I need to find the probability of calculating placing of r balls into n urns, such that there can be no empty urns.
I find the number of ways to do it is .
But this is pretty useless. It does not give me the actual probability.
For example, for n=2, r=3.
We can list down all the cases:
The probability is 6/8.
The number of ways is 6.
Using the formula, I get:
, which is pretty much meaningless.
Can I use any mathematical models to get the number 6, instead of having to list all down?