In Regents of the University of California v. Bakke, Allan Bakke, a 35-year-old white student, was twice rejected from the University of California Medical School. He believed the University of California was in violation of the 14th Amendment's "equal protection" clause and the 1965 Civil Rights Act because his grade point average and test scores were higher than those of any minority student accepted during the two years he applied. The school reserved 16 out of 100 openings for minority students, and therefore, Bakke argued, his rejections were based solely on his race.

The Court was largely mixed in its response. Four Justices believed that any governmentally-supported quota system was unconstitutional. Four Justices (including Thurgood Marshall) believed that the "purpose of overcoming substantial, chronic minority under-representation in the medical profession is sufficiently important to justify [a quota system.]" The remaining justice (Powell) agreed that rigid use of racial quotas was a violation of the 14th Amendment, but he conceded that race could be permissible as one of several factors in determining admission.