The correct answer is: Only II is implicit.
The statement “All are cordially invited to attend the entertainment programme. It is free.” does not provide any information about whether people generally go to entertainment programmes which are free. It also does not provide any information about whether generally, a free entertainment programme is of a good quality. However, the statement does provide information about the fact that some people, though interested in entertainment programmes, cannot afford purchasing the tickets. This is because the statement says that the entertainment programme is free, which implies that people who would not be able to attend the programme if it were not free are now able to attend. Therefore, the only assumption that is implicit in the statement is assumption II.