An admissions committee is hereby created in each county in the state. The admissions committee in each county shall be appointed by majority vote of an appointing board in each county consisting of the judge of probate of the county, two members of the county commission, who shall be selected from among themselves, and one member of the governing body of each of the two largest incorporated municipalities in the county, who shall be selected by the governing bodies of such municipalities from among themselves. In the event there is only one incorporated municipality in the county, two members of the appointing board shall be selected by the governing body of such municipality from among themselves. Of the members of the admissions committee first appointed in each county under the provisions of this section, one shall be appointed for a term of one year, one shall be appointed for a term of two years and one shall be appointed for a term of three years. Successors to the members of each admissions committee first appointed under the provisions of this section shall serve for a term of three years each. Members of the admissions committee in each county shall be residents and qualified electors of the county, but no member of such committee shall hold any public office of trust or profit or be actively engaged in the practice of medicine. The admissions committee shall meet at least once each month and may hold such other meetings as the committee deems necessary. Members of the committee shall receive no compensation for the performance of any duties imposed upon them under the provisions of this article.