Within days after the effective date of the formation of a district, a board of trustees shall be appointed as follows: (

a) In the case of a district that contains only unincorporated territory in a single county, the board of supervisors shall appoint five persons to the board of trustees. (

b) In the case of a district that is located entirely within a single county and contains both incorporated territory and unincorporated territory, the board of supervisors may appoint one person to the board of trustees, and the city council of each city that is located in whole or in part within the district may appoint one person to the board of trustees. If those appointments result in a board of trustees with less than five trustees, the board of supervisors shall appoint enough additional persons to make a board of trustees of five members. (

c) In the case of a district that contains only unincorporated territory in more than one county, the board of supervisors of each county may appoint one person to the board of trustees. If those appointments result in a board of trustees with less than five persons, the board of supervisors of the principal county shall appoint enough additional persons to make a board of trustees of five members. (

d) In the case of a district that is located in two or more counties and contains both incorporated territory and unincorporated territory, the board of supervisors of each county may appoint one person to the board of trustees, and the city council of each city that is located in whole or part within the district may appoint one person to the board of trustees. If those appointments result in less than five persons, the board of supervisors of the principal county shall appoint enough additional persons to make a board of trustees of five members.