**Core Concept**
The posterior interosseous nerve (PIN) is a branch of the radial nerve that supplies the muscles of the extensor compartment of the forearm, except for the extensor carpi radialis brevis. Injury to the PIN results in weakness or paralysis of finger extension, while sparing wrist and elbow extension.

**Why the Correct Answer is Right**
The posterior interosseous nerve arises from the radial nerve at the level of the elbow and runs down the forearm to supply the extensor muscles of the fingers, excluding the extensor carpi radialis brevis. The PIN is responsible for innervating the extensor digitorum, extensor indicis, and extensor digiti minimi muscles, which are responsible for finger extension. Since the PIN is responsible for finger extension, injury to this nerve would result in the inability to extend the fingers. However, the wrist and elbow extension, which are primarily innervated by the radial nerve itself, remain intact.

**Why Each Wrong Option is Incorrect**
**Option A:** Radial nerve injury would result in weakness of both wrist and elbow extension, which is not the case in this scenario.

**Option B:** Median nerve injury would result in weakness of thumb opposition, flexion of the fingers, thumb, and wrist, which is not consistent with the symptoms described.

**Option C:** Ulnar nerve injury would result in weakness of intrinsic hand muscles, leading to claw hand deformity, which is not consistent with the symptoms described.

**Clinical Pearl / High-Yield Fact**
The posterior interosseous nerve is a branch of the radial nerve that is prone to injury due to its deep location in the forearm, making it susceptible to compression or trauma.

**✓ Correct Answer: D. Posterior interosseus**