Calculate the number of students enrolled and finished within each month - powerbi

Question

I am trying to produce a cluster column chart with Month/Year as the x-axis and the number of enrolled and finished students within each month as y-axis, which would look like this (navy: enrolled students, red: finished students; A: April, B: May, etc):
In EXCEL, what I want to do would be simply put as:
Number of Enrolled = COUNTIFS('Student Enrolment Date', '>=01/04/2021', 'Student Enrolment Date', '<=01/04/2021')
Number of Completed = COUNTIFS('Student Finish Date', '>=01/04/2021', 'Student Finish Date', '<=01/04/2021')
Then use the calculated values to produce a visual.
The data example (let's call it Student) is as below:
I have also produced a date dimension as below:
I get confused about how to do this using DAX. If I connect Student['course start date'] with Date['Date'], and use Date['Year-Month'] as x-axis as below, then Power BI will count all students whose Student['course start date'] fall into each month. But because students is not necessarily get enrolled and finished in the same month, this method is apparently incorrect.
My questions are:
I am now trying to count the date in Student['student enrolment date'] and Student['student finish date'] within each month using:
Student Complete = COUNTROWS(FILTER(Student, Student[Status]="Complete" && Student[student enrolment date]>=DATE(2021, 4, 1) && Student[student enrolment date]<=DATE(2021, 4, 30) + 0))
but DAX says this is not a correct formula, and I don't know how to make this formula calculate for each month. Could you please correct me?
In my case, how to properly connect the date dimension to the Student dimension?

Answer 1

I think your model is not ok and that's why your DAX is much more complicated than necessary.
Create a fact table that connects your dimensions.
e.g. factStudentEvents
StudentId dateId Enrollments Completions
----------- ----------- ----------- -----------
1 20210413 1 0
1 20210620 0 1
2 20210427 1 0
Like this your DAX measures are very simple:
Completion Count = SUM(factStudentEvents[Completions])
Enrollment Count = SUM(factStudentEvents[Enrollments])