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Which sentence is 'grammatically' right?

ex1) The problem of who should pay for something

ex2) The problem of who to pay for something~

I think we can use both sentences.

The explanation in my workbook says that the sencone one is wrong because when the question word is 'who', we can not say who + to infinitive?!

I know, the second one('who to pay for something') sounds somewhat strange even to ME.

But, how can we say that the second one is 'grammatically' wrong?
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The problem of who should pay for something = the problem of who is to pay for something.

(The problem of who to pay for something means something different. You don't know who you should pay the money to.)
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Hello

I once had the same question you are raising. We can say any of "how to do", "where to do", "when to do", "what to do", "which one to do", and "whom to do", but we cannot say "who to do" (Note that here "who" is subjective "who", not objective "who" - the substitute for "whom", which Nona suggested).

Why? It is because these phrases are made by moving the WH-word in the phrases of a form "to do WH-word?" which the speaker has in their mind. That is;
"how to do" comes from "to do how?",
"when to do" comes from "to do when?",
"what to do" comes from "to do what?",
"whom to do" comes from "to do whom?", etc..
You will know easily that all of these WH-words in the phrases "WH-word to do" are actually either an adverbial or an object of the verb"do" when the speaker creates it in their mind.

But in the case of "who to do", the speaker cannot create such a phrase like "to do who?" in his mind because in English a subject must come before verbs.

paco