Another balls and bins problem, but I couldn't find one like this after browsing a while.
Say I have $N$ balls of $R$ different colors (N/R balls of each color) and I need to put them into $R$ different bins so that each bin have an equal number of ball (so $N$ is divisible by $R$). How many ways are there to distribute the balls?
edit: Assume that $N > R$ , for example, if we want to put $36$ balls of $4$ different colors (9 balls of each color) into $4$ bins so that each bin always has $9$ balls, how many ways are there to do it?