The local public finance authority shall be governed by a board of directors. The board of directors shall consist of the following members:

1. (a) Five members of the county boards of supervisors.

2. (b) Five members of governing boards of school districts in the county.

   1. (1) Governing board members shall be selected in a manner determined by the county board of education, provided that:

      1. (A) If there are five or more school districts in the county, no school district shall have more than one member on the board of directors.
      2. (B) If there are fewer than five school districts in the county, each school district shall have at least one member on the board of directors.
   2. (2) For purposes of this subdivision, the county office of education shall be deemed to be a school district.