Xの担当 - something X is in charge of OR something in charge of X?

Question

Can Xの担当 have both of these meanings?

If so, then without context to disambiguate the two meanings, is one of the two more commonly used?

For example, how would you translate the sentence Xの担当を決めたら？To me, it could be either "How about you decide who is in charge of X?" or "How about you decide what X is in charge of?" If both are grammatically valid translations, then is one of these more commonly used than the other, or do you have to completely rely on context to decide which one?

Also, this is a vague followup, but does the answer to this question also generally apply to the construction (noun)の(verb)? Does NのV mean "something that N does V to" (N is subject) and "something that does V to N" (N is object)?

Answer 1

You are exactly right: it can be translated as "whatever X is in charge of" or "whoever is in charge of X." Thus,

Xの担当を決めたら？

can be both "How about deciding what X is going to be in charge of?" and "How about deciding who's going to be in charge of X?" To give an example,

掃除の担当を決めたら？

is "How about deciding who's going to do the cleaning?" and

太郎の担当を決めたら？

is "How about deciding what Taro is going to be in charge of?"

As for whether this applies in general, I believe it doesn't. Off the top of my head, I can't really come up with a different word that can be an attribute of both a person and a non-living thing. Also, I feel like "Xの担当" is a noun as a set and not a combination of noun and verb (I might be wrong about that).