Final answer:
The correct answer is B) Open listing and exclusive-agency listing, where property owners can sell their property on their own without owing commission to the listing broker.
Step-by-step explanation:
The question deals with different types of real estate listings and the implications of each for the property owner in terms of the obligation to pay commission to a real estate broker. The types of listings mentioned are open listing, exclusive-right-to-sell listing, and exclusive-agency listing.
An open listing allows a property owner to list their property with multiple brokers and still retain the right to sell the property themselves without paying any commission. With an exclusive-agency listing, the property owner also retains the right to sell the property themselves without owing a commission, but this type of agreement differs from an open listing in that it gives only one broker the right to sell the property. On the other hand, an exclusive-right-to-sell listing requires the owner to pay the listing broker a commission regardless of who sells the property, even if the owner sells the property personally without the broker's help.
Thus, the correct answer to the student's question is B) Open listing and exclusive-agency listing, as these are the two types of listings that allow property owners to sell their property on their own without the obligation to pay a commission to the listing broker.