Refluxing, say, one mole of 1,5-dibromo-pentane with excess ammonia in ethanol can result in the formation of rings. (e.g. $1\lambda^2$-piperidine)
However, it is also possible for the 1,5-dibromo-pentane molecules to be connected together, forming longer chains without forming rings. The longer chains can be reacted again to form larger rings. So in theory, we can have rings that are arbitrarily large.
This is about the rings' size distribution
Question: What is the expected number of rings (large and small) after the reaction finishes? How many of the rings are $1\lambda^2$-piperidine? Generally, is there a mathematical distribution that describes the expected number of rings of any given size?