Final answer:
The question references the University of Kentucky's women's basketball team's success in the early 1920s, including an undefeated season, but it mistakenly asks about the women's cross-country team, for which there is no information provided. Additionally, in 1924, the university disbanded their women's sports teams, aligning with societal norms of the era.
Step-by-step explanation:
The question seems to be about a historical fact related to women's sports teams at the University level. However, there appears to be a misunderstanding in the question as it mentions the University of Kentucky women's basketball team, instead of a cross-country team, and refers to a specific period during the early 1920s. It is stated that the University of Kentucky women's basketball team had an undefeated season and was considered one of the best in the nation during the early 1920s.
Unfortunately, there seems to be no direct information regarding the number of championships won by the women's cross-country team in their school history. Moreover, in 1924, the University of Kentucky followed a widespread trend of disbanding their women's teams due to the belief that competitive team sports were not appropriate for women during that time.