First, may I point out that you are using the wrong character for the apostrophe. You are using a grave accent `, whereas it should be (in ordinary computing use) the same character as you use for the single quote ' "Julia has three weeks' holiday" has no article for the same reason that "Julia has Angela's pen" has no article. The possessive noun functions as a determiner, so we don't need another one.
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Paul EvdokimovWhat`s happened with an article in 'Julia has got three weeks` holiday'? I mean, why can`t/shouldn`t we put any before `three weeks`?There are two different versions of this: