**Core Concept**
The external auditory canal (EAC) is a complex anatomical structure lined by skin and cartilage, and its innervation is crucial for understanding pain perception and surgical procedures in this area. The posterior wall and floor of the EAC are supplied by a specific nerve branch that originates from the cranial nerve responsible for facial sensation.

**Why the Correct Answer is Right**
The posterior wall and floor of the EAC are supplied by the auriculotemporal nerve, a branch of the mandibular division of the trigeminal nerve (cranial nerve V). The auriculotemporal nerve carries postganglionic parasympathetic fibers from the otic ganglion, which are involved in the innervation of the parotid gland, but it also provides somatic sensation to the posterior wall and floor of the EAC. This nerve branch is responsible for transmitting pain and temperature sensations from these areas.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because it does not accurately represent the nerve supply to the posterior wall and floor of the EAC.
**Option B:** This option is incorrect because it is not directly related to the nerve supply of the EAC.
**Option C:** This option is incorrect because it is not a recognized nerve branch that supplies the posterior wall and floor of the EAC.

**Clinical Pearl / High-Yield Fact**
It is essential to remember that the auriculotemporal nerve is a branch of the mandibular division of the trigeminal nerve, and its involvement in the innervation of the EAC is crucial for understanding the sensory supply of this area.

**Correct Answer: C. Auriculotemporal nerve**