Final answer:
The correct sentences that follow the rules of coordination and subordination are A) Nicolle loves working with little children and hopes to be an elementary teacher after she finishes college, and C) Nicolle loves working with little children, and she hopes to be an elementary teacher after she finishes college.
Step-by-step explanation:
The correct sentences that follow the rules of coordination and subordination are: A) Nicolle loves working with little children and hopes to be an elementary teacher after she finishes college. C) Nicolle loves working with little children, and she hopes to be an elementary teacher after she finishes college.
In sentence A, the coordinating conjunction 'and' is used to join two independent clauses. In sentence C, a comma is used to separate the independent clauses. Both sentences demonstrate proper coordination and subordination.