1. Whitey in Roumania

Whitey's master died 5 years ago. However, he has been waiting for him.

2. Whitey in Roumania
Whitey's master died 5 years ago. However, he has waited for him for a long time.

3. Whitey in Roumania
Whitey's master died, but, he has been waiting for him for 5 years.

4. Whitey in Roumania
Whitey's master died, but, he has waited for him for 5 years.
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Which short passage is right?
Can we use all the passages?
is "Whitey" a rude word?

Starting a sentence with a conjunction (and, but, however, etc.) is not considered proper grammar. We do it sometimes, but it's not "correct". Sentences three and four use the conjunction more correctly, but no comma is needed after the conjunction.

"Whitey" is not a bad word if it is the servant's or pet's name or nickname. If it is in reference to someone's skin color, it could be offensive.

As I said, beginning a sentence with a conjunction is common. Traditionally, it was thought to be a grammatical error, but has become more acceptable.

I must respectfully disagree with Writeacher about pronouns. I see no problem. It seems clear to me that "he" and "him" are clearly and properly used. Writeacher is not wrong. The sentences could be clearer, but I don't see a terrible problem as you have written them.

1. Whitey in Roumania

Whitey's master died 5 years ago. However, he has been waiting for him.

2. Whitey in Roumania
Whitey's master died 5 years ago. However, he has waited for him for a long time.

3. Whitey in Roumania
Whitey's master died, but he has been waiting for him for 5 years.

4. Whitey in Roumania
Whitey's master died, but he has waited for him for 5 years.

All four passages convey the same information, but with slightly different sentence structures. None of them are inherently incorrect, but some may be more grammatically preferred than others depending on the context and style.

1. "Whitey's master died 5 years ago. However, he has been waiting for him."
2. "Whitey's master died 5 years ago. However, he has waited for him for a long time."
3. "Whitey's master died, but he has been waiting for him for 5 years."
4. "Whitey's master died, but he has waited for him for 5 years."

You can use any of these passages to convey the idea that Whitey's master passed away and Whitey has been waiting for him.

The word "Whitey" itself is not inherently rude. It is a name or nickname given to a person or animal. However, it's important to use names respectfully and responsibly, as certain names can be considered derogatory or offensive in specific contexts or cultures.