I've heard both of these before.
- All the good people
- All of the good people
Are they both correct?
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Both correct! They both have the same meaning. The "of" variant is a partitive genitive, like French bouteille de vin (bottle of wine). I'd say "all of" has a connotation of "all members of group x", whereas "all" without "of" is completely neutral, just the entirety of x. In most cases either connotation will result in the exact same meaning.