Explanation:
> "If he had entered the room, I ____ him."

This is a third conditional sentence, which describes a hypothetical situation in the past (an unreal event that didn't happen). The structure of a third conditional is:

If + past perfect, would have + past participle.

Now, let's look at each option:

- A. saw — This is simple past tense, but it doesn't fit the third conditional structure. Incorrect.
- B. had seen — This is the past perfect, but we need "would have seen" in the main clause to complete the third conditional structure. Incorrect.
- C. would have seen — This is the correct third conditional form: "If he had entered the room, I would have seen him." This fits the sentence perfectly. Correct.
- D. may see — This is present tense and doesn't fit with the hypothetical past situation. Incorrect.
- E. will see — This is future tense, which doesn't match the past hypothetical context. Incorrect.