Good! Now, in certain situations you may also want to include DISTINCT in your CASE WHEN statements with COUNT. Take a look:

SELECT
  COUNT(DISTINCT CASE
    WHEN pay_date BETWEEN '2015-06-01' AND '2015-06-05'
      THEN candidate_id
  END) AS accepted_student,

  COUNT(DISTINCT CASE
    WHEN pay_date = '2015-06-06'
      THEN candidate_id
  END) AS conditionally_accepted_student,

  COUNT(DISTINCT CASE
    WHEN pay_date > '2015-06-06'
      THEN candidate_id
  END) AS not_accepted

FROM application;

What changed here? Two things. First of all, we included the keyword DISTINCT in each COUNT. Second, we now count student_ids and not pay_dates. What is the meaning of these changes?

We previously counted the number of accepted payments, conditionally accepted payments and not accepted payments. Now, we count the number of candidates who were accepted for at least one degree course, the number of candidates who were conditionally accepted for at least one degree course and not accepted for at least one degree course.

We had to include the keyword DISTINCT because a single candidate can apply for more than one degree course, so if a candidate made two payments for two courses on time, that candidate would be counted twice (the candidate can be still counted twice in two different columns if the candidate paid for one degree course and didn't pay for another, but that's a different story).