An alternative form of county government shall include a board of county commissioners, elected either at large as provided in sections 302.04 and 302.08 of the Revised Code, or by districts as provided in sections 302.041 and 302.082 of the Revised Code, and in all those provisions of sections 302.01 to 302.24 of the Revised Code, which have not been specifically designated as applicable only in the case whereby the entire board is elected at large, or in the case whereby any of the members are elected by districts.