Question

1. They are a professor and a writer.
2. They are a professor and writer.
3. They are professors and writers.
4. He is a professor and writer.
5. He is a professor and a writer.
(Which expressions are not correct?)

Answer 1

They are all correct. However, the exact sentence depends upon your meaning.

Answer 2

What about #5? Doesn't 'a professor and a writer' mean two persons?

Answer 3

No. The professor also may be a writer.