grammatical number - Subject singular or plural?

I got really confused reading conflicting grammar rules for sentences such as below:

• First one:

  
  
  

  
  

  A number of people is/are going to the party.

  
  

  
  
  

  Here, the subject is "A number". Since "A number" is plural, the the correct answer must be

  
  
  
  

  
  

  A number of people are going to the party.

  
  




• Second one:

  
  
  

  
  

  His collections of music is/are good.

  
  

  
  
  
  

  Here, the subject is "Collections of music". Since "collections" is a plural, the correct answer must be:

  
  
  

  
  

  His collections of music are good.

  
  




• Third one:

  
  
  

  
  

  His collection of music is/are good.

  
  

  
  
  
  

  Going by my previous rule, since the subject here is "collection of music", which is singular, the correct answer must be:

  
  
  

  
  

  His collection of music is good

  
  

But I have seen answers that state the right answer to the second one is "His collections of music is good".

Can someone please elucidate this?

Thanks in advance!

Answer

For the first one, the subject of the sentence is the whole noun phrase a number of people, in which a number of collectively acts as a determiner - a class of words that includes the articles a, an, and the as well as words such as many, most, and every - and people is the head word, which is the root noun which is being modified by the rest of the phrase. Compare to other sentences using related noun phrases with different determiners - for example, you wouldn't think twice about the correctness of "Several people are going to the party" or "Beautiful people are going to the party."

You can also verify this by noting that removing people from the sentence leaves you with "A number of is going to the party" - a nonsense sentence - whereas removing a number of leaves you with the workable sentence "People are going to the party." Even if you take out the of as well, to get "A number is going to the party," it still doesn't make sense unless you're living in some kind of cartoon world; it conjures up images of an anthropomorphic number 7 as the guest of honor.

For the second and third, you're in the right. "His collections are good" and "His collection is good" are the correct forms. My only guess for why you might have seen otherwise is that maybe someone misread the second statement and didn't notice that collections was pluralized, as one normally refers to the entirety of a person's music library as a singular collection.