**Core Concept**
The question tests the knowledge of the clinical presentation of ulnar nerve injury, specifically the symptoms and signs related to the ulnar nerve's distribution in the hand.

**Why the Correct Answer is Right**
The ulnar nerve is responsible for innervating the intrinsic muscles of the hand, including the interossei and the hypothenar muscles. The loss of extension of the little and ring fingers is due to the ulnar nerve's innervation of the extensor digiti minimi and extensor indicis proprius muscles. The hypothenar atrophy is a result of the ulnar nerve's innervation of the hypothenar muscles, including the adductor pollicis, flexor digiti minimi, and opponens digiti minimi. The metacarpophalangeal joint hyperextension is due to the imbalance between the flexor and extensor muscles of the hand, which is caused by the ulnar nerve injury.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the median nerve is responsible for innervating the thenar muscles and the muscles of the anterior forearm, and is not associated with the symptoms described.

**Option B:** This option is incorrect because the radial nerve is responsible for innervating the extensor muscles of the wrist and fingers, and is not associated with the symptoms described.

**Option C:** This option is incorrect because the musculocutaneous nerve is responsible for innervating the muscles of the anterior forearm, and is not associated with the symptoms described.

**Clinical Pearl / High-Yield Fact**
In ulnar nerve injuries, the "claw hand" deformity is a classic sign, characterized by hyperextension of the metacarpophalangeal joints and flexion of the interphalangeal joints of the ring and little fingers.

**Correct Answer:** C. Ulnar nerve injury.