I'm trying to calculate the number of ways we can distribute $n$ prizes among $m$ people. However, we require that the winner receives at least as many prizes as the runner-up, we require that the runner-up receives at least as many prizes as the 3rd player, and so on.
Also we must distribute all the prizes. Also there might be more prizes then people, but not less.
If it weren't for the requirement, it would be a simple binomial coefficient. However, how do I calculate the possible distributions with the requirement? Not sure how to start.
My idea is to take the number of distributions without the requirement and then subtract something, but I don't know what to subtract.
Thanks for the help!