Within thirty days after entering the final order establishing the district, the department shall enter an order appointing the board of directors named in the petition in accordance with subsection (5) of section 46-516. After the selection of the original board of directors of a district as provided for in subsection (5) of section 46-516, their successors shall be elected as provided in section 32-516. Elections shall be conducted as provided in the Election Act and shall take office on the first Thursday after the first Tuesday in January next succeeding their election. Qualified electors of the municipality or municipalities within the territory which composes the territory of a district shall be qualified electors of such district. A qualified elector of a subdivision may only cast his or her ballot for a director to be elected from such subdivision.