I have seen how different sites in a multisite Drupal installation can have contrib modules that other sites in the multisite do not. These site specific modules go inside the specific site's directories which are in the sites directory.

But if there are contrib modules that are to be common to all the sites in a multisite is there a way to locate them in the sites/all directory instead of each site having its own copy of the same code?

Can each site of a multisite have a different set of core modules enabled if they are all using the same database?