The correct answer is: Only I and III are implicit.
The statement says that ten candidates who were on the waiting list were admitted to the course. This does not mean that wait-listed candidates do not ordinarily get admission, as it is possible that some wait-listed candidates are admitted each year. It also does not mean that a large number of candidates were on the waiting list, as it is possible that only a few candidates were on the waiting list and all of them were admitted. However, the statement does imply that the number of candidates to be admitted is small, as otherwise it is unlikely that all of the wait-listed candidates would have been admitted.
Assumption I: Wait-listed candidates do not ordinarily get admission.
This assumption is not implicit in the statement. The statement does not say anything about whether or not wait-listed candidates ordinarily get admission. It is possible that some wait-listed candidates are admitted each year, or it is possible that no wait-listed candidates are ever admitted.
Assumption II: A large number of candidates were on the waiting list.
This assumption is also not implicit in the statement. The statement does not say anything about how many candidates were on the waiting list. It is possible that only a few candidates were on the waiting list, or it is possible that a large number of candidates were on the waiting list.
Assumption III: The number of candidates to be admitted is small.
This assumption is implicit in the statement. The statement says that ten candidates who were on the waiting list were admitted to the course. This implies that the number of candidates to be admitted is small, as otherwise it is unlikely that all of the wait-listed candidates would have been admitted.