The correct answer is C. Marginal mandibular branch of the facial nerve
Step-by-step explanation:
The marginal mandibular branch of facial nerve connects in the lower lip and chin, this nerve affects movement and sensations in the bottom lip, the lower corner of the mouth and part of the chin. Due to this, it is common if this nerve is damaged it leads to distorted facial expression, especially a distorted smile, as well as drooling in the bottom lip.
According to this, it is likely the nerve that was damaged in the 45-year-old woman is the marginal mandibular branch of facial nerve because this nerve is the one related to the inner lip and the lower corner of the mouth, and therefore the one that would cause drooling or constant dripping of saliva from the right margin of her mouth in the case it is damaged.