There are 31 pairs of spinal nerves: 8 cervical nerves, 12 thoracic nerves, 5 lumbar nerves, 5 sacral nerves and 1 coccygeal nerve.

Each nerve separates from the spinal cord and exits the spine through the intervertebral foramen found between adjacent vertebrae. The nerves innervate regions of the peripheral nervous system and relay information to and from the central nervous system.

A dermatome is an area of skin innervated by the cutaneous branches of a single spinal nerve. When spinal nerves diverge from the spinal cord, they innervate regions of the periphery and serve to relay information between the periphery and central nervous system. T10 innervates tissue around the level of the umbilicus, or navel. The C4 spinal nerve innervates the top of the shoulder, T4 innervates the level of the chest, T7 innervates slightly lower at the level of the xiphoid process, and L1 innervates the inguinal region around the groin.

The arm has a few major veins that drain it. The brachial vein drains the deep portions of the arm, the basilic vein drains the medial superficial portion of the arm, and the cephalic vein drains the lateral superficial portion of the arm. The brachial and basilic veins join in the armpit (axilla) to form the axillary vein.

The vertebral arteries serve to supply blood to the posterior head. They also run into the skull and branch together into the basilar artery. This artery runs along the cerebellum and supplies it and the brain stem with oxygenated blood. 

The aorta has three crucial segments. The aortic arch is the beginning of the aorta, where it exits the left ventricle. Three blood vessels branch from the aortic arch: the brachiocephalic artery, the left subclavian artery, and the left common carotid artery. Around the T4 vertebra the aortic arch transitions into the thoracic aorta. The thoracic aorta has four major branches: the intercostal, bronchial, esophageal, and phrenic arteries. After the thoracic aorta, the vessel transitions into the abdominal aorta.

The vertebral arteries come off of the subclavian arteries, which branch off of the aortic arch (left) and brachiocephalic artery (right).

The recurrent branch of the median nerve innervates the lateral two lumbricals and the thenar muscles. Damage along any part of the median nerve will result in the "papal sign" when the patient is asked to make a fist.

The ulnar nerve divides into the deep and superficial branches when it terminates in the hand. The deep branch innervates the third and fourth lumbricals, while the superficial branch innervates the palmaris brevis. The radial nerve innervates several structures, including the biceps brachii and triceps brachii.

Compression of the radial nerve in the axilla due to poorly fitted crutches is also known as crutch palsy and causes the pins and needles described in the question.

The median and unlar nerves primarily serve to innervate the hand and wrist, while the musculocutaneous nerve is more involved with forearm movements at the elbow.

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.