Learn English – “People persons” versus “people people”

Persons is very rare in normal English speech. Mostly you only come across it in legal or other "official" contexts such as...

The defendant conspired with a person or persons unknown to blow up the House of Lords.
6 persons maximum/Licensed to carry 4 persons (notices on lifts/taxis).

In most normal contexts the plural of person is people. When making a restaurant booking, for example, you'd normally ask for a table for six people - if you said six persons that would suggest you're nervous, unfamiliar with such situations, and foolishly trying to sound "correct" in an inappropriate context. If it was a swanky restaurant they might just say they're fully booked because you sounded gauche.

Individuals is also relatively uncommon in speech, tending again to be restricted to official (particularly, written) contexts. Probably because of this, if you said you saw four individuals somewhere, it might well imply four suspicious-looking characters, since the phrasing is typical of witnesses giving evidence in court, rather than everyday conversation.

Note that individuals carries no connotations of each individual being significantly different to every other. Identical twins wearing similar clothes are still two individuals, if the context permits using the term at all.

There's more on this subject in Person, Persons, People, Peoples, which was asked previously on ELU, but for most purposes I suggest it's enough to note that the standard forms are person/people.

As the definite article, "the" indicates an exact example of the noun it modifies.

Did you pet the dog?

Did you pet a dog?

In the first example, there is a specific dog that is the object. In the second, it could be any dog.

The carpenter repaired the legs of the tables.

The carpenter repaired legs of the tables.

This one is a little more tricky, but the same rule applies.

First, the tables means that there are a specific set of tables being discussed.

In the first sentence, the legs means that he/she repaired:

• All of the legs of all of the tables
• OR, all of the legs of all of the tables that required repair.

In the second sentence, this is ambiguous. The carpenter definitely repaired some of the legs. Because it is plural, they repaired more than one leg. However, whether it was all of the (repairable) legs or not, we cannot say.

Many good students will buy that book.

In this sentence, many operates as a determiner*. It describes good students. However, its meaning is ambiguous in the following areas:

• Possibly, not all students are good students. Students who are not good are not considered - they may or may not buy the book, but are not part of the set the sentence is discussing.
• Probably, not all good students will buy that book. Otherwise, the sentence would say "All good students will buy that book."
• "Many good students" are not a specific set.

That said, if you intend the third meaning you could say "The many good students will buy that book." But this has a different meaning:

All of the [many [good students]] will buy that book.

In other words:

• There are good students.
• There are many good students.
• All members of this set will buy the book.

* A determiner or quantifier (link courtesy of choster) is a word that describes a noun or noun clause, telling us whether it is specific or general. The definite article ("the") is a determiner, as are indefinite articles and many other words that describe the specificity of the noun.