There is hereby established in the division of occupational and professional licenses a state board of dentistry to be composed of eight (8) members, five (5) of whom shall be dentists, two (2) of whom shall be dental hygienists, and one (1) of whom shall be a member of the public with an interest in the rights of consumers of dental services. Board members shall be appointed by the governor and shall serve at the pleasure of the governor. Upon appointment by the governor, the term of office of a member of the board shall commence on the first Monday of February following his appointment and shall continue for five (5) years, or until his successor has been named, whichever is later. A vacancy in membership of the board shall occur whenever the regular term of a member expires or when a member dies, resigns or is removed from office by the governor. Appointments to fill a vacancy occurring for some reason other than expiration of term of office shall be made for the unexpired term which is being filled.