The first option is used if you are referring to a plural, for example if you were talking about making a meal for a group of girls you would say the girls' dinner. The second option is used when referring to a singular so I would say that b) is correct. Sorry probably not much help as it contradicts the other answers given, I will check with my brother who is an English teacher.
Bot are acceptable - it used to be that you could only miss out the s on a possessive name ending with an s if it were a saint's name, eg St Nicholas' church. Nowadays, 's is used for everything apart from Jesus. (are such things done in Jesus' name?)
So, Charles's book - which is how you'd say it - is fine, as is charles' book, but it looks a bit pedantic and old fashioned now.
There's loads about it in Eats, Shoots and Leaves.