let's say I have k empty slots and N different sources to fill these spots.
A source can put as many elements in the slots as possible (from 0 to k), and all slots have to filled
How many different possibilities are there of filling all the slots? For instance such a combination would be : for k = 5, N = 3, 3 comes from source 1, 2 from source 2, 0 from source 3. The problem is simple for N=1,2,3 but I can't find a simple formula to express this number.
Is it a very well known formula that I'm missing? thanks