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If I want to convey the message that has the meaning as follows

We are going to find the right job for each student.

I would like to ask which one is better and why?

  1. We are going to find the right jobs for the students.
  2. We are going to find the right job for the students.

The rule is that the student can have only one job and we are going to find only one job for each of them. If I use the first choice, my concern is that it seems possible to imply the many to many relation? (Esp. many jobs for one student, which is not desirable.) But also the second choice might imply that I am going to find only one job for all students.

Another similar case might be the situation where I see a lot of umbrellas which belong to students but only one umbrella per student. Should I say "The umbrellas of the students or the umbrella of the students".

Or it might be the case that the language is ambiguous and to use something like "the umbrella of each of the student." is unavoidable in order to be specific.

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    Your unnumbered version is better than either of the numbered ones.
    – Lawrence
    Commented Apr 25, 2017 at 14:43

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Let's start with your rules:

  1. The student can have only one job.
  2. We are going to find only one job for each of them.

Now examine each sentence:

First sentence

We are going to find the right jobs for the students.

Your concern about this sentence:

If I use the first choice, my concern is that it seems possible to imply the many to many relation? (Esp. many jobs for one student, which is not desirable.)

Yes it is possible to imply a many-to-many relation. You have more than one job and more than one student and you haven't specified that each student will be placed in only one job. Most people would understand that you are going to place each student into a single job from this phrase however, because this is typically how employment works, one person per job. However there is certainly scope for this sentence to be interpreted how you have mentioned (many to many relationship) from the perspective of the grammar.

Second sentence

We are going to find the right job for the students.

You have just one job here (job is singular) and many students, and you are finding the job for the students. You have one job and therefore the implication is that you will place more than one student into it.

The first sentence then is definitely better, because while ambiguous it does at least allow the possibility for the interpretation you are seeking (that you will place each student into an individual job).

The sentence you opened your question with:

We are going to find the right job for each student.

Is however the best for your intended meaning because you are mapping an individual job with each individual student.

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    On the first sentence, "the right jobs for the students", it certainly could be used to mean a many-to-many, as in the case of "There are so many little tasks to be done, but we will find the right jobs for the students." That is, each student will have multiple jobs, but they'll be the right ones for that student. And the second option could definitely be considered as a group activity -- you've got a bunch of botany students, so give them the job of cleaning up the garden. If it were a bunch of engineering students, have 'em fix the elevator. I too like the original option best.
    – Roger Sinasohn
    Commented Apr 25, 2017 at 14:24

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