When do you change a word into a different case?

Question

I was given this sentence

Сегодня мы с Джулией собираемся в поездку в Россию по программе обмена студентами.

• по программе — dative
• обмена — genitive
• студентами — instrumental

Why are these all in different cases? I understand that after по, nouns have to be in the dative case, but I don't know why exchange is put in the genitive, and students is in the instrumental.

The way I thought it worked is that everything referring to the initial thing you're talking about will be put in the same case, and since program is in the dative, I thought everything else would be dative, too.

Is there a general rule I can follow to understand when to put a word in a specific case? I'm really confused on how that works — especially in this sentence.

I would love as much information and as many tips as you can offer to help me with this.

Answer 1

It's because every word is governed by the word that precedes it:

1. The preposition по in this sentence governs the dative. That's why программа is in the dative

2. Обмен is in the genitive because it answers the question программа чего? That is, of what? - of the exchange

3. Студенты is in the instrumental because the verb обмениваться, of which обмен is a derived noun, governs the instrumental case - обмениваться кем/чем?, and by extension обмен кем/чем?

Putting студенты in the genitive would misrepresent the intended meaning of the phrase because обмен студентов in Russian may mean either an exchange made by students and NOT an exchange between students or an exchange of students for someone/something other than their peers.

The genitive of the following noun doesn't convey the meaning of reciprocal exchange of students because it makes the noun обмен a derived noun of the verb обменивать rather than обмениваться. Обменивать in its turn, doesn't govern the instrumental case.

So basically, we have обмен кем/чем? and обмен кого/чего? and they mean different things.

The only rule is to follow the cases that convey the meaning relevant to a phrase or a sentence, which, of course, needs to be studied, learned and memorized.

Answer 2

С Джулией - instrumental. В Россию, в поездку - accusative.

The words you mentioned are not homogeneous members of the sentence. Try to say it in English and you'll see how differently the relations between the words are expressed.

If you need a table of the Russian cases and how they're used, here you are:

http://expressrussian.com/wp-content/uploads/2016/12/1-russian-cases.png

But that's not the best way to learn them correctly. The cases are best studied one by one, very gradually, for different types of declensions and for different cases of usage.