Archaeologist: There were several porcelain-production centers in 18th

Here's how I approached it:

First, a two second summary of archaeologist claim: Because porcelain cups have unique compositions, archaeologists can use composition analysis to determine where the next discovered cup comes from.

So looking at the statements, I try to eliminate the statements that do not support the archaeologist's claim:
a) RELEVANT: Says that they have previous porcelain cups, so these are the cups that they could use for their composition analysis
b) ELIMINATE: Cups that are not made of porcelain do not support his claim
c) RELEVANT: The next cup has to be porcelain, archaeologist only talks about identifying cups that are porcelain
d) ELIMINATE: Hurts archaeologist claim because it introduces reasoning to why composition analysis might not lead to correct origin of cup
e) ELIMINATE: Hurts archaeologist claim because composition analysis might not point to correct origin if two origins produce the same type of composition
f) ELIMINATE: Seems like irrelevant information

So between A and C, it's not too hard to tell which one is the archaeologist assumptions and which one is possible fact. The archaeologist is assuming that they can find out where the next cup comes from because the next cup will be porcelain, and they can use composition analysis. The fact that all of the cups they have previously found were porcelain strengthens the assumption that the next one will be porcelain as well.

If you reversed it, and said that the assumption is all of the past cups found were porcelain, the possible fact that the next one will be porcelain does nothing to strengthen your assumption.

The question seems quite straightforward.
Conclusion is that the origin of the next cup discovered can be easily determined.
Going through the answer choices we can find that the argument clearly assumes that the next cup to be discovered would be made of porcelain. Although we can also apply the LEN method : The next cup to be discovered need not be porcelain. This clearly kills the argument. So "C" is the right answer.
Now we have to select a choice which as a fact could strengthen the assumption. We can see that choice "A" clearly strengthens this assumption.

Fact 1: 18th-century Britain had several porcelain-production centers.
Fact 2: Each center developed a unique recipe for its porcelain.
Fact 3: There is an archaeological site.
Assumption: They will be able to recover cup from this archaeological site.
Assumption: Cup from this archaeological site will be made in Britain.

A: Other cups have been recovered from the archaeological site, all of which were made of porcelain.
Cannot be inferred from above facts or assumption.

B:Some of the cups recovered from the archaeological site were not made of porcelain.
Cannot be inferred from above facts or assumption.

C:The next cup to be recovered from the site will likely be maid of porcelain.
Cannot be inferred from above facts or assumption.

D:Porcelain makers often traveled between centers, experimenting with one another's recipes.
Cannot be inferred from above facts or assumption.

E:There was considerable overlap of materials in the recipes used by the various centers.
Cannot be inferred from above facts or assumption.

F:Most porcelain in 18th century Britain was made at one of the several centers.
Can we inferred from Fact 1, although word Most is bit of a stretch.

C:The next cup to be recovered from the site will likely be made of porcelain.: Possible fact to support assumption
F:Most porcelain in 18th century Britain was made at one of the several centers.: Assumption.

Am I correct?