Which classification of joint is NOT part of the primary classifications?

The classification of joint referred to as "ball-and-socket" is a specific type of synovial joint but does not represent a primary classification of joints. The primary classifications, which categorize joints based on their structure and mobility, include fibrous, synovial, and cartilaginous joints.

Fibrous joints are characterized by the dense connective tissue that holds the bones together, with little to no movement. Cartilaginous joints allow for more movement than fibrous joints but less than synovial joints, as they are connected by cartilage. Synovial joints, on the other hand, are known for their wide range of motion and includes several subtypes determined by their shapes and movements, such as hinge, pivot, and ball-and-socket.

Ball-and-socket joints, such as the hip and shoulder joints, are just one specialized category within the broader synovial classification. Therefore, the answer correctly identifies "ball-and-socket" as not being a primary classification of joints.