are de and des the same when it comes to plural denotation?

Question

for example,
is combien de livres Y a-t-il dans votre sac
the same as combien des livres Y a-t-til dans votre sac?

Answer

Bonjour Patrick,
Typically "de" is singular and "des" is plural, After reviewing the lesson, Il y a beaucoup de chats the beaucoup de is a "fixed" expression, if you will meaning a lot of followed by the plural noun chats.   
J'espère que ma réponse vous aiderez.
Ron

Answer

Bonjour Patrick !

In the cases of "combien de, beaucoup de..." , "de" is actually the preposition "of" and as it's not followed by the article "les", it simply doesn't contract in "des".
As you know "des" in French can be both the plural of "un/une":  
un chat / des chats  = [some] cats
or the contraction of the preposition "de" (of/from) + "les" (the):  
la mère des enfants = the mother of the children
Il vient des États-Unis = He is from the United States

I hope that's helpful!
À bientôt !