I am asked:
Randomly tossing $nlg(n)$ balls into $n$ bins, find $C$ such that $\text{Pr}(\text{No bins containing more than } Clg(n) \text{ balls}) \ge 1-\frac{1}{n}$.
I'm thinking that using Markov's Inequality, the probability of one bin having more than $Clg(n)$ balls is smaller than $\frac{1}{C}$. If all bins are independent, then
$$(1-\frac{1}{C})^n\ge1-\frac{1}{n}$$
would give the result, but I am not sure if bins are independent of each other. I am wondering if there're any alternatives to finding $C$.