Final answer:
The vinegar-based BBQ sauce option is Carolina Gold BBQ, which reflects the East Carolina style, although it also incorporates mustard influence from South Carolina.
Step-by-step explanation:
The BBQ sauce offered for ribs that is vinegar-based is typically associated with East Carolina style, where the sauce is a combination of vinegar and hot pepper. From the choices given, c) Carolina Gold BBQ would be the closest match for a vinegar-based sauce, as Carolina-style BBQ is known for its vinegar and pepper roots, although the 'Gold' often indicates a mustard influence, likely from South Carolinian tradition. This mustard-based sauce is thought to have been introduced by Germans who migrated to South Carolina a century or more ago.