"Twenty two students"
Translation:Двадцять два студенти
You use «студенти» with numerals ending in «два» '2', «три» '3', «чоти́ри» '3' (please note that двана́дцять 12, трина́дцять 13, and чотирна́дцять 14 are formed irregularly, and end in -дцять, which is a form of десять 'ten', so you use «студе́нтів» with them).
With numerals ending in «оди́н» 'one', you use «студе́нт» (please note, again, that одина́дцять 11 is irregular and ends in -дцять).
With all the other numerals (ending in 5, 6, 7, 8, 9, 0, 11, 12, 13, 14, 15, 16, 17, 18, 19) you use студе́нтів.
This rule might seem complicated; it's related to the language history. In the past, Ukrainian has 3 numbers, singular, dual and plural. Now we don't have dual number, but different form for 2, 3, 4 is a remntant of the times when we had it.
The rule might seem complicated, but it's the same for all the nouns. If you learn it for «студе́нти», you'll learn how to choose the correct form for all the other nouns too.
(I have no idea why dual was used not just with numerals ending in 2, but also with 3 and 4.)
Standard Ukrainian doesn't have the word «двадесять». While it is indeed an original form of «два́дцять», we don't use it now and I think most people would be surprised to see it written this way.