Como diferenciar palavras contáveis de incontáveis em inglês

Well, to give a more comprehensive answer I would need more time.

But the quick and dirty tip is as follows, look up into this site:
http://www.englishclub.com/vocabulary/n ... e-list.htm

You can´t find "vocabulary" and "illness" in it, what narrows your search to just two words.

Both has a countable and uncountable meanings, but if I had to choose I would pick the letter d) vocabulary/baggage. Because "vocabulary" in sense (2) can be C or U. So there´s more possibility of using it as countable than the other word.

Others will pick e) paper/illness because of illness (it can be pluralized
as well - as in: mental illnesses...etc)


http://dictionary.cambridge.org/diction ... ?q=illness
http://dictionary.cambridge.org/diction ... vocabulary


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So, the alternatives D and E are possible to my thinking.
I already found multiple choice questions that accepted two choices, anyway it is not the rule, rather the exception. So for the time being, in my view, the question wasn´t well elaborated.
I may be mistaken, tough.


Note: Some of the other given words (of the question) might have a uncountable and countable sense, depending on the context as well.
I didn´t made a foray into that aspect not to confuse things more.

Complemento:

O link a seguir traz boas explicações sobre o assunto:

• Substantivos contáveis e incontáveis em inglês

Bons estudos!

Thank you very much!