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I am trying to grasp the difference between de and des after nouns and “beaucoup”.

  1. I am aware of the construction beaucoup de (always singular) + nouns.

    J'ai beaucoup de livres.

    J'ai peu de défauts.

    What is the rule behind the use of just "de" ? Any other cases like this? Can we say that this applies for adjective/adverb?

  2. After nouns, I saw

    Justificatif de domicile

    Nombre d'écrans

    Why are we using “de” here ? Why not “justificatif du domicile” or “nombre des écrans”? What is the rule here?

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Several constructions exist that link two nouns with the preposition de.

  1. The preposition de can be used to characterize the kind of object we are talking about. It is in this case used without an article, and the following characterization can either be singular or plural.

    le sac de sable
    le sac de fraises

    This is what happens with “justificatif”.

    le justificatif de domicile

    You can think of it as a single word, like “brosse à dents”.

  2. Other usages of de exist, for example, to express possession (but not only). In this case:

    • to form an indefinite reference use d'un/d'une (preposition de + article) + noun

      le sac d'un ami

    • to form a partitive (or indefinite plural) reference use de (preposition de, alone) + noun

      plusieurs sacs d'amis

    • to form a singular definite reference to an object use du/de la/de l' (preposition de + article) + noun.

      le sac du facteur

    • to form a plural definite reference to particular objects use des (preposition de + les) + noun (plural form).

      le sac des élèves

The funny thing is that many of your examples (“beaucoup”, “peu”, “nombre”) are very particular examples, because each corresponds to two different fixed locutions. The first ones are very similar to first type of constructions:

  • beaucoup de bateaux: a lot of boats
  • peu d'élèves: few students
  • nombre d'instituteurs: numerous teachers

The second ones act as a particular kinds of pronouns and are quite similar to the second type of constructions as they refer to a definite set:

  • beaucoup des bateaux (que …): many of/among the boats (which …)
  • peu des élèves (que …): few of/among the students (whom …)
  • nombre des candidats (que …): a large number of/among candidates (whom …)

It is also possible to use un/le nombre as a usual noun. In this case it has to be preceded by an article and it means “number”. It is followed by a bare de:

  • le nombre de participants: the number of participants

It's similar for un/le peu which means “a/the little” (and can also be used for some uncountable plurals):

  • un peu de sable
  • un peu de fraises
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  • I don't understand the second part where you write "beaucoup des bateaux". It seems not right, so if you can give example, it would be nice.
    – Yohann V.
    May 20, 2015 at 12:53
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    @Yohann: Beaucoup des bateaux que j'ai vus avaient une coque bleue.
    – Stéphane Gimenez
    May 20, 2015 at 13:48
  • It is crystal clear like this, thank you
    – Yohann V.
    May 20, 2015 at 13:52
  • Thanks Stéphane. It seems that beaucoup de, peu de, nombre de are more of the total number in general, where with des , it means more of certain individuals in the collection ? What would mean number of students , as in the number of students in the class is 10 ? Can we safely say that noun1 + de + noun2 always hold true if noun2 characterizes/complement noun1 and not noun1 of noun2 ?
    – Kenny
    May 20, 2015 at 16:14
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    In “sac à sable” the meaning is “made for”; “en” would be used for “made of” like in “sac en papier”. Though sometimes “de” can also be used for that, like in “pont de pierre”. “Bureau de tabac” is clearly not a usual “bureau”; this is another good example.
    – Stéphane Gimenez
    May 21, 2015 at 11:24

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