Learn Russian: В институте триста студентов. - There are three hundred students at the institute.

Good catch! The numbers 2, 3, and 4 do take the genitive singular. However, the hundreds 200, 300, and 400 take the genitive plural. Because of this rule, we use the plural студентов instead of the singular студента.

Where is the verb 'are' in this sentence?

In Russian, the present tense of the verb 'to be' is almost always left out. The sentence literally translates to 'In the institute three hundred students,' but it naturally means 'There are three hundred students at the institute.'

Why does триста end in '-а' instead of just being 'три сто'?

The Russian words for 300 and 400 are built by combining the first digit with the genitive singular form of сто (one hundred), which is ста. They merge into one word, creating триста.

Why do we use the preposition в here for 'at' instead of на?

We use в (in/at) with институте because an institute is a standard enclosed building and institution. The preposition на is generally reserved for events, open spaces, or specific exceptions like на факультете (at the department) or на работе (at work).