On one point the Court ruled 5-4 that state universities may not set aside a fixed quota of seats in each class for minority members, denying white applicants the opportunity to compete for those places.
On a second point the Court ruled 5-4 that admissions officers do not violate the equal protection guarantee when they consider race as one of many factors that determine which applicant is accepted and which rejected.
To see the entire University of California Regents
v. Bakke decision.
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