Not sure what I have wrong in this Oracle SQL query, I've asked my professor but the stuff he has told me to try isn't working

I am trying to get a count of how many students enrolled per month and this is my current query:

SELECT registrationdate AS "REGDATE", COUNT(*) AS "NUMSTUDENTS"
  FROM registration r
  INNER JOIN students s
  ON r.studentid = s.studentid
  GROUP BY To_Char(registrationdate, 'Month')
  ORDER BY NUMSTUDENTS;

If I take registration date out of select then it will work, showing the correct number of students separated by month however the actual month column itself is missing at that point. Error I am getting is a "SQL Error:

> ORA-00979: not a GROUP BY expression
>
> 00979. 00000 - "not a GROUP BY expression""

You wrote

SELECT registrationdate AS "REGDATE", ...

which is not an aggregate (like COUNT) and does not appear in the GROUP BY.

You wanted to write

SELECT To_Char(registrationdate, 'Month') AS "REGMONTH", ...

This may help you understand why.

Suppose three students registered on February 6th
and another pair on February 8th.
So we're reporting a single "February" row with a count of five.
Is it meaningful to report the five events as
happening on the 1st, or the 28th, or the 6th, or the 8th?
No.
We are aggregating at the month level,
and the report rows should reflect that.