Five students visit three farmers in their village. Here, What do "their" refer to - students? or farmers?? and Why? and Why not?
As numerous people have pointed out in comments, their could refer here to students, or farmers, or both.
It's normal for a written sentence to be ambiguous; but even in speech, this sentence is unclear.
And this kind of ambiguity is common with pronouns (among other things).
The reason is actually a very simple one, which applies to many other grammatical phenomena as well. Since it's so simple, however, it's unavoidable, and causes lots of difficulty.
The reason why it's ambiguous is because information is being left out, and sometimes
-- actually, pretty often -- the information being left out is crucial for avoiding ambiguity.
What's being left out?
- Every time a pronoun is used instead of a noun, information is left out.
- Every time a that goes missing from a clause, or a to from an infinitive, information is left out.
- Every time one clause is missing stuff because it's already been said, information is left out.
Et cetera. All those short cuts are lossy. And they can lead to ambiguity.
This is a basic principle of legal English, for instance, since ambiguity
has to be carefully negotiated in the law.