Hello and Happy Easter for everyone. I would to kindly ask for your help to the following exercise: We would like to share 50 chocolates of the same type and put them in 10 different boxes (not necessarily in equal sharings). With how many ways can we do this, depending that no box will be empty?
I would like to ask whether it is a problem of combinations, because I started to solve it as a problem of combinations.
Thank you very much in advance.
To be found is number or tuples $(a_1,\dots,a_{10})$ where the $a_i$ are positive integers that satisfy $\sum_{i=1}^{10}a_i=50$.
This can be done by applying stars and bars.
Give it a try.