The palmar digital branches of the median nerve are responsible for cutaneous innervation of the palmar side of the thumb, index finger, middle finger and half of the ring finger.

The superficial branch of the ulnar nerve innervates the palmaris brevis, while the deep branch of the ulnar nerve innervates the third and fourth lumbricals. The radial nerve innervates several structures including the biceps and triceps brachii.

The two medial lumbricals are innervated by the deep branch of the ulnar nerve. The lateral two lumbricals are innervated by the digital branches of the median nerve.

The other answer choices show correct muscle-nerve pairings.

The skier likely compressed her superficial peroneal nerve which innervates the dorsum of the foot.

The superficial peroneal nerve wraps around the neck of the fibula and is a common site of compression when people cross their legs or wear high boots.

The plantar surface of the foot is innervated by the tibial nerve, which courses through the posterior leg. The lateral aspect of the foot is innervated by the sural nerve, which arises from the tibial nerve. The first dorsal web space of the foot is innervated by the deep peroneal nerve, which arises from the common peroneal nerve and runs in the anterior leg. The medial aspect of the leg is supplied by the saphenous nerve, which arises from the femoral nerve.

The lateral femoral cutaneous nerve supplies the lateral thigh and is highly visible during the anterior approach to the hip as it lies between the sartorius and the tensor fasciae latae. The lateral femoral cutaneous nerve is part of the lumbar plexus and arises from spinal root L2.

The medial leg is supplied by the saphenous nerve, which arises from the femoral nerve. The groin area is supplied by the ilioinguinal nerve, arising from L1. The anterior leg is innervated by the common peroneal and superficial peroneal nerves, arising from the sciatic nerve. The plantar surface of the foot is innervated by the tibial nerve, which courses through the posterior leg and also arises from the sciatic nerve.

Maxillary is a branch of the trigeminal nerve (V), and not of the facial nerve (VII).

The branches of the facial nerve, from superior to inferior, are: temporal, zygomatic, buccal, mandibular, and cervical.

The latissimus dorsi muscle is innervated by the thoracodorsal nerve and functions to extend, adduct, and medially rotate the humerus. Damage to the thoracodorsal nerve would result in diminished capacity to pull the body up, such as during climbing or doing pull-ups.

The dorsal scapular nerve innervates the rhomboid and levator scapulae muscles. The accessory nerve innervates the sternocleidomastoid and trapezius. The intercostal nerves innervate the thoracic cavity and some upper extremity regions.

The pectoralis major is innervated by both the medial and lateral pectoral nerves. In contrast, the pectoralis minor is only innervated by the medial pectoral nerve. 

The long thoracic nerve innervates the serratus anterior muscle. The superior and inferior pectoral nerves are false answer choices and do not refer to anatomical structures.

The biceps brachii is innervated by the musculocutaneous nerve. The muscle is located anterior to the humerus and functions as a primary flexor of the forearm at the elbow.

The median nerve innervates muscles of the anterior compartment of the forearm, the muscles of the thenar eminence in the hand, and the first and second lumbricals of the hand. The median nerve runs through the carpal tunnel and, when compressed, is responsible for the symptoms of carpal tunnel syndrome. The radial nerve innervates the muscles of the posterior compartment of the arm and forearm. The axillary nerve innervates the deltoid, teres minor, and triceps brachii.

The brachial artery is the major blood vessel of the upper arm, derived from the axillary artery after it passes the glenohumeral joint. After passing the elbow joint, the brachial artery bisects into the radial and ulnar arteries, which supply blood to the forearm. Inflating the blood pressure cuff around the upper arm compresses the brachial artery.

The radial nerve innervates the muscles in the posterior compartment of the arm and the posterior compartment of the forearm, responsible for extension of the arm and forearm. These include the medial and lateral heads of the triceps brachii, brachioradialis, supinator, and the extensor muscles of the forearm (extensor carpi radialis longus, extensor carpi radialis brevis, extensor carpi ulnaris, extensor digitorum, and others).

The musculocutaneous nerve supplies the anterior compartment of the forearm, innervating the coracobrachialis, the biceps brachii, and the brachialis muscles. The median nerve innervates muscles of the anterior compartment of the forearm, the muscles of the thenar eminence in the hand, and the first and second lumbricals of the hand. The axillary nerve innervates the deltoid, teres minor, and triceps brachii muscles.