The word 'origin' is an uncountable noun but it has a plural form. Is this use of the word 'origin' correct?
Solution 1:
Please look up various existing threads here on non-count and count nouns. As CGEL says, it's very unhelpful to consider nouns as inherently count (consider the non-count usage of coffee, say:
"Coffee is my favourite drink")
or non-count (now consider
"Two coffees, please" and "The two most widely grown coffees are arabica and robusta").
It's usages that are either count or non-count. Many nouns can swing both ways.
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With 'origin', the picture is even more complex. Both the singular and plural forms are available, taking the expected agreement (origin is; origins are), but as Longman says, they are usually interchangeable (unlike say coffee / coffees).
Note also that Longman does say that 'origin' can be used in both count and non-count [(C,U)] ways. The count usage (do not confuse this with the common non-count plural form; we wouldn't say "My 5 ethnic origins are in South-east Asia") is rare. I've found an example in a scientific article from Proceedings of the National Academy of Sciences of the United States of America, PNAS:
Two of the three replication origins in each species were located in the vicinity of a cdc6/orc1 replication initiation gene ...
As might be expected, the count usage focuses more precisely on an origin / source / birthplace than the more inclusive, general non-count usage. But the broader, more general (perhaps 'fuzzier' is too pejorative) sense is what is usually the more convenient one.
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Here, examples 1,4,5 and 8 are ungrammatical. 'Interchangeable / synonymous' yes ... but the required verb-form may need adjusting.
2 and 3 seem conceptually muddled (origin/origins are usually non-sentient; 'originator' would be somewhat better).
While 6 and 7 are both acceptable, 7 is more commonly found according to Google Ngrams. However, the plural-form variant might well be preferred to hint strongly at complex, detailed beginnings. And note that 'beginning/s' behaves rather similarly.
The Cambridge English Dictionary gives more detail on when the plural- or singular-form non-count usage might be (or must be) preferred.
(a) It's a book about the origin/s of the universe.
either totally acceptable and idiomatic.
(b) Her unhappy childhood was the origin of her problems later in life.
the plural form would not co-exist happily with 'was', required by the subject.
(c) He is of North African origin. / (d) What is your country of origin?
of origin, not of origins.
(e) We begin our dip into local history by examining the town's origins.
arguably the more idiomatic, strongly connoting (at least) a complex early history
(f) The Easter egg has both pagan and Christian origins.
certainly needs the plural form, but I'd argue against this being a count usage. 'The Easter egg has several origins, both pagan and Christian' doesn't work. 'Origins' is more unitary, an agglomeration here. Note that 'The Easter egg has origins both pagan and Christian' is perfectly grammatical if a little rarefied.