Noun form at the end of a sentence with many objects

Question

If there is a high school student and a university student.

Can we say,

There are a high school student and a university student.

or

There is a high school student and a university student.

or

There is a high school and a university student.

or

There are a high school and a university students.

But if one group is greater than one. Let's say

There is a high school student and three university students.

Can we say,

There are a high school and three university students.

or

There are a high school student and three university students.

or

There is a high school student and three university students.

I am confused here how to make the sentences right according to the grammar rules.

Answer 1

In academic writing, the plural form "there are" should be used whenever the following noun phrase is plural. However, most other writing is much more lax about this, and you'll often find "there is" or "there's" being used with plural noun phrases, especially when the first element by itself is singular.

It seems this issue was a big deal over at EL&U: "“There Is”/“There are” depends on plurality of the first list element or not?"

The third, fourth, and fifth sentences you asked about are all incorrect.

Most style guides recommend you avoid syntactic expletives (there is/are/was/were) altogether and favor a different sentence construction.