Looks like you need at least one more table:
Students::__pkStudentID = Registration::_fkStudentID
Classes::__pkClassID = Registration::_fkClassID
This way different students can register for different groups of classes by creating records in Registration that link the student to each of the selected classes.
For an explanation of the notation that I am using, see the first post of: Common Forum Relationship and Field Notations Explained