If adjustment schools are organized by only one county or city and county, the government and management shall be vested in a governing board which shall be either the board of education, or similar school governing body, or the county probation committee of the juvenile court, or a board of trustees composed of seven members selected from both the board of education and the probation committee, as may be determined or chosen in the exercise of sound discretion by the board of supervisors or other governing body of the county or city and county.