"both of" is must be used with plural pronouns: 1. Both of them 2. Both of us 3.
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Eq:
"both of" cannot be used with bare plurals (plural nouns without an article):
5d. *Both of dogs
6d. *Both of parents
Paco:
[1] Why 'both of' cannot be used with bare plurals?
'They' and 'both' in "they both" are appositional just like 'we' and 'Japanese' in "we Japanese" are..
the result of googling is: 154,000 hits for "they both are ... " and 1460,000 for "they are both... ". So I have to admit the latter should sound more natural to native speakers.