Regents of the University of California v. Bakke, (1978) started when Allan Bakke applied to the University of California Medical School at Davis in 1973 and 1974. He was rejected both years.
The school policy said for every hundred students admitted sixteen of the students must be minority students. Bakke's qualifications (scores and GPA) were higher than every one of the minority students admitted during both of the years that he applied but he was overlooked so that the minority quotas were filled.
He took the school to court saying that the school's actions violated the 14th amendment's equal protection clause and Title VI of California's Civil Rights Act of 1964. He argued that the university had overlooked him solely on the basis race. The case went from the California courts (who ruled in favor of Bakke) to the Supreme Court.