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The mix of sports I saw in the park also made me think of Melbourne's mix of people/peoples.

Hi,

Would you use people or peoples in the above? Thanks.
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Hard to say-- how various are they?
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If you mean a mix of different kinds of people in the sense of tall people, short people, smart people, stupid people, happy people, sad people, and so on, you need people.
If you mean a mix of different peoples in the sense of ethnicities and/or cultures (the Chinese people, the Japanese people, the African people, and so on), you might want to use peoples.
That said, the phrase mix of peoples puts me in mind of ancient migrations of tribes. I think of the large migrations of large nation-like groups thousands of years ago. Different ethnic and cultural groups encountered one another during these migrations, often creating "a mix of peoples".
Given this mental association of mine, I would choose people, not peoples, in your example sentence. Melbourne may be large, but it can't compete with the world as a whole as a place where different peoples interact with one another.

CJ
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Thanks, Mister.

What do you mean by "How various are they?"

I think it should be the plural "peoples" because there are more than at least one people, but the original uses the singular "people." Could you shed some light?
 CalifJim's reply was promoted to an answer.
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Thanks, Jim.

I'm still confused. In my mind, there are at least two different kinds of people mixing there, whites and aboriginals, let alone Asians and those from other cultures.