## Generalised Birthday Paradox - bins problem

We are putting balls into bins by the Uniform Distribution. Let $X$ be a Random Variable and means moment of collision when two balls fall into the same bin. So minimum $X$ is 2 (2 balls in the same bin) and maximum $X$ is $n+1$. What is probability $P(2 \le X \le n+1)$ and Expected Value for $k$ bins and $n$ balls?