How does carry in work in full adders?
The rows do not indicate any kind of sequence or relationship. This is simply a table of 3 inputs (A, B, CarryIn) and two outputs (Sum, CarryOut). We could put the rows in any order and it wouldn't matter.

Simply count the number of 1 bits in the three inputs. If there are two or three ones then the CarryOut will be 1, else it is 0. It there are one or three ones on the inputs then Sum will be 1, else it is 0.