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executive secretary

Posted: 28 Jun 2022, 08:47
by Lone
When I look up my dictionaries for 'executive secretary', I found the below 2 examples:

She’s executive secretary to New York University’s president.
He was executive secretary of the NAACP.

I have 3 questions on my mind.
1) The dictionaries say 'executive secretary' is countable. So why is the article 'an' absent before 'executive secretary' (i.e. She's an executive secretary to ...)?
2) Since 'executive secretary' is a title, it should be a proper noun. Shouldn't the first letter be capitalized (i.e. Executive Secretary)?
3) What is the proper preposition after secretary? I note that the first example use 'to' whereas the 2nd example use 'of'.

Thank you very much!