In my previous question titled "Conditional combinations of balls in bowls", is there a distribution to fit $k$ when $d \gg M$? I mean, when $d$ is so large, what is the distribution of the total number of balls?
$M$ can be a number between $4$ to $64$ and $d$ (number of bowls) is very large, about $10000$. Each bowl can have $0,1,2,\ldots,M$ balls in it with equal probability. What is the distribution of total number of balls $k$? $\Pr(k=k_0)=$?