$k = \sqrt n$ balls are thrown into $n$ bins. The bins are standing in a row and numbered from 1 to $n$. What is the probability that there are no two balls in the same bin or in adjacent bins???
In other words the probability that the distance between every two balls is at least one bin.
I'm not sure how to even begin solving this. If a ball lands on the end then the next ball has only 2 places where it cannot land. But if a ball lands not on the end then the next ball has 3 places and now I have up to 2 more ends to contend with. I tried drawing a probability tree but very quickly got lost.