(a) The said board may consist of five members, all of whom shall be bona fide residents of and qualified electors of such school districts and who shall be appointed by either the board of supervisors, the governing authorities of the municipality, or by both of said bodies in such proportion as the governing bodies may agree upon. The first such board shall be appointed so that one trustee shall be appointed to serve for one year, one for one year longer, one for two years longer, one for three years longer, and one for four years longer. Upon the expiration of each such original term, each appointment shall be for five years and shall be made by the authority making the original appointment. In case of the occurrence of a vacancy, the authority which made the appointment of the trustee responsible for such vacancy shall appoint a successor to serve the remainder of the term of such trustee.

(b) In case of a special municipal separate school district which embraces the entire county, the board of trustees may be constituted and selected in accordance with the terms and provisions of Sections 37-7-707 through 37-7-711, with the exception that one member of such board shall be elected by each supervisors district and shall be a resident and qualified elector of the district from which he is elected.

(c) In case of a special municipal separate school district embracing the entire county, the board of trustees may be constituted and selected in accordance with the terms and provisions of Section 37-7-713.