(2) is wrong. Judging by your subsequent question, I suspect you may have intended to type "their birthday". "their birthdays" is natural here.
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teacherJapanThank you very much for your quick answer:) What about "birthday" by itself without "their?"You mean "Westerners celebrate birthday regardless of their age"? No, that is incorrect.
teacherJapanWhat about "birthday" by itself without "their?"Singular countable common nouns require a determiner, so you can't do that.