Are options the same as alternative possibilities?

When it comes to theorizing about choice, should we distinguish between having multiple options and having alternative possibilities of action?

Suppose a deterministic agent takes a multiple choice test. Consider a specific choice between a, b, c, and d. Suppose further that the agent chooses c. Did the agent have multiple options? It seems so; after all, can't they be clearly seen to be printed on the test? All the agent has to do is circle one! This is, I think, importantly different from a case in which there is only one candidate answer, say a, printed on the test. In neither of these cases is there a possibility of the agent choosing anything other than what they actually choose, because the agent is deterministic. But in spite of that, it seems to me that cases are not on a par; there is something present in the former which is absent in the latter, and this something has implications concerning the agent's freedom (or lack thereof) in choosing as they do.

From this somewhat deflationary perspective, the fact that more than one choice is given for an agent's consideration or that more than one choice influences an agent's course of deliberation is of itself sufficient for their having multiple, genuine options. (Having alternative possibilities of action might also be sufficient for having multiple, genuine options, but on this view it is not necessary.) If that's so, determinism is compatible with an agent's having multiple options, even though they couldn't do otherwise. The question is then whether an agent's having multiple options--along with such background conditions as being rational and knowing the difference between right and wrong--is sufficient for having free will or moral responsibility. I'm interested to see if you think it is sufficient, and if not, what more is required.