Each county is authorized to hold one county fair in each year, or, as an alternative, to participate with any other county or counties in the holding of a district fair. Where counties participate in the holding of a district fair, the boards of county commissioners of each of participating counties may enter into mutual agreements setting forth the manner and extent of the participation by each county in the management and support of the district fair, subject to the limitations imposed on each respective county by the provisions of this chapter.