**Core Concept**
The question is testing the knowledge of nerve anatomy and its relation to common injury patterns. The correct answer requires understanding of the anatomy of the lower limb and the nerves that supply it.

**Why the Correct Answer is Right**
The patient is lying in a right lateral position with injuries to the right arm and knee. This suggests that the patient may have fallen onto their right side, potentially compressing or stretching nerves in the right lower limb. The lateral aspect of the right knee is a common site for injury to the common peroneal nerve, which is a branch of the sciatic nerve. The common peroneal nerve runs laterally around the fibular head, making it susceptible to injury in this location.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because the median nerve is more commonly associated with injuries to the arm, wrist, or forearm, rather than the knee.
* **Option B:** This option is incorrect because the ulnar nerve is more commonly associated with injuries to the elbow or cubital tunnel, rather than the knee.
* **Option C:** This option is incorrect because the femoral nerve is more commonly associated with injuries to the hip or thigh, rather than the knee.

**Clinical Pearl / High-Yield Fact**
The common peroneal nerve is often injured in falls from a height, where the knee is forced laterally, compressing the nerve against the fibular head. This is a classic mechanism of injury for common peroneal nerve palsy.

**Correct Answer: C. Common peroneal nerve**