We examine the participation in secondary and tertiary education of five cohorts of Danish males and females who were aged twenty starting in 1982 and ending in 2002. We find that the large expansion of secondary education in this period was characterized by a phenomenal increase in gymnasium enrollments, especially for females. Not only did the educational opportunities for individuals with disadvantaged backgrounds improve absolutely, but their relative position also improved. A similarly dramatic increase in attendance at university for the period 1985-2005 was found for these cohorts when they were aged 23.