The board of barber examiners must consist of three members, each of whom must be appointed by the governor for a term of three years. The terms of office of the members must be so arranged that one term expires on the thirty-first day of December of each year. Each appointment must be made from a list of five names submitted to the governor by the state barber association, and each member must be a registered barber who has followed the occupation of barber in this state for at least five years prior to that member’s appointment.