Sec. 8. (a) Whenever a vacancy occurs on a board, the city board of health shall provide to the appointing authority a list of five (5) individuals, at least three (3) of whom must have professional experience in one (1) of the following areas:
(1) Medicine.
(2) Nursing.
(3) Health care administration.
(4) Pharmacology.
(5) Dentistry.
(6) Veterinary medicine.
(7) Engineering.
(8) Environmental science.
(9) Social work.
(10) Legal profession.
(11) School administration.
(b) The list must include at least one (1) licensed physician. When filling a vacancy, the appointing authority may select from the list provided by the city board of health.