In Brown v. Board of Education, the Supreme Court declared segregation in public schools unconstitutional.
This decision overturned Plessy v. Ferguson (the decision that supported separate but equal, so choice 1 is incorrect) and declared that racially segregated schools were unconstitutional. As well, it specifically concerned state-sponsored schools, so choice 2 is also incorrect. Lastly, though it paved the way for integration, it didn't order it, so choice 4 is incorrect. Ultimately, choice 3 is the best because Brown v. the Board of education did deem segregation in state sponsored schools to be unconstitutional.