Final answer:
The glossopharyngeal nerve (ninth cranial nerve) supplies everything in the back of the throat except for the stylopharyngeus muscle, which is also innervated by the ninth cranial nerve.
Step-by-step explanation:
Everything in the back of the throat is supplied by the glossopharyngeal nerve (ninth cranial nerve), except for the stylopharyngeus muscle. The stylopharyngeus muscle, which is involved in elevating the pharynx during swallowing, is uniquely innervated by the cranial nerve IX, also known as the glossopharyngeal nerve. This nerve is responsible for the contraction of muscles in the tongue and throat, part of the sense of taste, and the production of saliva. It is also involved in the act of swallowing, as it coordinates the muscles that help guide food from the mouth through the pharynx and into the esophagus.