I've recently encountered this message: "Invalid arguments' number". My brain has immediately corrected it to "Invalid number of arguments", but this got me thinking about the nuances of using the Saxon genitive here.
My intuition is that the use of Saxon genitive for a plural noun implies that each of the entities in the plural set is separately in some relation described by the genitive phrase, and not that the genitive refers to the whole set as one entity.
Is my intuition correct? Are there any popular examples of this specific difference between Saxon genitive and the "of" preposition?