定員 and 人数: a capacity limit and the actual count
Compare a course’s capacity with its stated participant count and read the condition behind closure when capacity is reached.
The prescribed capacity
定員, read ていいん, is the prescribed capacity in people. この講座の定員は三十人です。 states a capacity of thirty for this course.
That capacity alone does not establish thirty actual participants. It gives the basis for how many can be accepted.
The stated count of people
人数, read にんずう, means the number of people. 今回の参加人数は二十人です。 states twenty participants on this occasion.
With capacity thirty and participation twenty, the prescribed capacity and actual count differ. Do not turn the capacity figure into an observed participant count.
Reaching capacity and closing registration
参加者が定員に達したため、受付を終了しました。 reports closing registration because participant numbers reached capacity. The reason for closure is explicit.
受付を終了しました。 alone does not identify reaching capacity as the reason. Check the participant condition and registration status sentence by sentence.
Does 定員は三十人です。 alone establish thirty participants on this occasion?
Show the answer and why
No. 定員 is the capacity. The actual count needs separate information or a tally.