I have $n$ sets and $k$ elements with $k\gt n$. Each elements has the same probability $\left(\frac1n\right)$ to be inserted in a set. All the elements have to be inserted in one single set.
I need to calculate the probability the difference of number of elements between the fuller set and the emptier one is at least $X\%$.
For example, given $10$ sets and $100$ elements I need to calculate the probability one sets has at least the $10\%$ of elements more than another.