The City Council shall have the power to establish a Personnel Board and to appoint the members thereof to serve without compensation, to administer a personnel system under rules and regulations to be made by the Council. Such Board shall, among other things, provide for the classification of all employments in the administrative service of the City not excepted by the provisions of this Charter, by the Council, or by the people, for open, competitive and free examinations as to fitness, for an eligible list from which vacancies shall be filled for a period of probation before employment is made permanent, and for promotion on the basis of merit, experience and record.