The "Stars & Bars" technique has proven very helpful in solving various combinatoric problems I have been dealing with. I have been able to tweak it slightly to fit various examples, but one form still elludes me:
Is there a formulaic answer when there is a general/global maxium?
Ex: if you have 15 balls; how can you sort them into 10 bins, if each bin is only capable of holding 4 balls maximum? (and how would the amount of combinations change if each bin could hold a max of 5 or some other number)
I have a feeling there is a formula out there to encompass or help with this but have been unable to find it. Thank you very much for any help you may have.
