1. I don't know who to hire.

2. I don't know whom to hire.
3. I don't know who I should hire.
4. I don't know whom I should hire.
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Are they all grammatical? Do we have to use 'who' or 'whom'? Which one is commonly used?

5. I don't know why to do that.
6. I don't know why I should do that.
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Is #5 correct? I think #6 is right.

Whom is the objective form, so since the person you will hire is WHOM you don't know, "whom" is correct. #6 is better than #5.

1. "I don't know who to hire." - This sentence is grammatically correct. The word "who" is used as the subject of the verb "to hire." It is commonly used in everyday speech and writing.

2. "I don't know whom to hire." - This sentence is also grammatically correct. In formal English, "whom" is the correct form when it serves as the object of the verb "to hire." However, in modern usage, "whom" is less commonly used and is often replaced with "who" in informal contexts.

3. "I don't know who I should hire." - This sentence is grammatically correct. The word "who" is used as the subject of the verb "should hire." It is commonly used in everyday speech and writing.

4. "I don't know whom I should hire." - This sentence is also grammatically correct. In formal English, "whom" is the correct form when it serves as the object of the verb "should hire." However, in modern usage, "whom" is less commonly used and is often replaced with "who" in informal contexts.

Regarding your additional questions:

5. "I don't know why to do that." - This sentence is not grammatically correct. The correct phrasing would be "I don't know why I should do that." The word "why" is used as a relative pronoun, and it requires a subject (in this case, "I") followed by a verb ("should do").

6. "I don't know why I should do that." - This sentence is grammatically correct. The word "why" is used as a relative pronoun, and it is followed by the subject "I" and the verb "should do." It is the correct and commonly used form.

1. "I don't know who to hire." - This sentence is grammatically correct. In this sentence, "who" is being used as the subject of the infinitive verb "to hire."

2. "I don't know whom to hire." - This sentence is also grammatically correct. In this case, "whom" is being used as the object of the infinitive verb "to hire."

3. "I don't know who I should hire." - This sentence is grammatically correct as well. Here, "who" is the subject of the verb "should hire."

4. "I don't know whom I should hire." - This sentence is also grammatically correct. "Whom" is the object of the verb "should hire."

The choice between using "who" or "whom" depends on whether it is being used as a subject or object in the sentence. "Who" is commonly used in informal contexts, while "whom" is more formal and may sound more appropriate in more formal writing or speech. However, in modern English, the use of "whom" is becoming less common, and many people use "who" in both subject and object positions.

5. "I don't know why to do that." - This sentence is not grammatically correct. The correct form would be: "I don't know why I should do that." Here, "why" is used as the object of the verb "know," and "I should do that" is the reason or purpose unknown to the speaker.

6. "I don't know why I should do that." - This sentence is grammatically correct. In this case, "why" is the object of the verb "know," and "I should do that" is the unknown reason or purpose.