Whichever ones you choose does not matter.
Which ones you choose does not matter
Sentence (1) is perhaps ambiguous. I think the Original Poster wants whichever ones you choose to be understood as an interrogative clause. In this case the sentence means something like:
- The answer to the question Which ones are you going to choose? is not important.
If this is what the Original Poster wants to say then we do not need the -ever suffix here. Sentence (2) is a much better sentence than sentence (1).
Notice that the whole interrogative clause which ones you choose is the Subject of the sentence. The noun phrase which ones is the Direct Object of the verb choose within the clause which ones you choose. It is not the Subject of the verb does. Because the whole interrogative clause is the Subject of the larger sentence the verb takes third person singular agreement:
- [Which ones you choose] does not matter.
You can compare this with a simpler sentence:
- [What she said] does not matter.
Notice that we cannot use plural verb agreement if the Subject of the sentence is a clause:
- *[What she said] do not matter. (ungrammatical)
Extra note 1:
It might be useful to know that native speakers do not like to use clauses as the Subjects of sentences. We find these types of sentences difficult to process. We often avoid this by using a dummy pronoun, the word it, as the Subject of the sentence and moving the clause to the end of the sentence where it will function as a Complement of the verb. If we do this with the Original Poster's sentence, we get:
- It does not matter [which ones you choose].
Extra note 2:
This sentence looks very similar to a conditional sentence:
- Whichever ones you choose, it does not matter.
This sentence has a very different structure to the one in the Original Poster's example. Here the Subject of the main clause is the pronoun it. The interrogative clause whichever ones you choose is functioning as an Adjunct in the sentence. It tells us the set of situations in which it does not matter. This type of sentence is called an exhaustive conditional. In exhaustive conditionals like this one, we definitely do need to add the suffix -ever to the interrogative word:
- *Which ones you choose, it does not matter. (ungrammatical)
Extra note 3:
It is possible—but unlikely—that in sentence (1) the phrase whichever ones you choose is a noun phrase. With this reading, this noun phrase is a special type of construction called a fused relative construction (or a free relative). If we read the sentence like this, it means:
- Those things that you choose do not matter.
In this sentence the phrase whichever ones you choose is a plural noun phrase headed by the plural noun ones. So the larger sentence now has a plural Subject and the verb do must take plural agreement:
- [Whichever ones you choose] do not matter.
Because it is in a fused relative clause construction, we have to put the suffix -ever on the relative word. With this intended meaning the following sentence is ungrammatical:
- *Which ones you choose do not matter. (ungrammatical)