"Three persons work here."
Translation:Тут працюють три людини.
The suggested translation is «три люди́ни», I believe it uses only the grammar taught in this course.
Троє is a different type of numeral. Три is a cardinal numeral, while троє is a collective numeral. They are only used when talking about groups of people, and there's a limited number of these numerals. 2 is двоє, 3 is троє; other numbers are formed with -еро suffix (4 четверо, 5 пʼятеро, 6 шестеро, 7 семеро, 8 восьмеро, 9 девʼятеро, 10 десятеро). They can't be made up of 2 or more words, so while you can have a number 20 два́дцятеро, you can't have a collective numeral 21 or 22. There are no forms bigger than 100.
Collective numerals are used with plural nouns in genitive. They can also be used with pronouns (нас дво́е 'two of us'). They are not usually used with feminine or neuter nouns.
It makes sense to focus on cardinal numerals because they're much more useful. You can paraphrase any sentence with троє using три, but not vice versa. So, I'd suggest you focus on learning the cardinal numerals first, and then revisit collective numerals after you're comfortable with the cardinal numerals.