"no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the united " how does this excerpt relate to the pemises of brown v. board of education?

The correct answer is: "the statement guarantees equal rights for all US citizens and prevents any removal of such privileges and immunities".

Brown v. Board of Education was a case that led to the enactment of a landmark decision by the US Supreme Court in 1954, which declared segregation unconstitutional.

The case was about the constitutionality of the "separate but equal" lemma that was accepted in a former decision enacted by the US Supreme Court in 1896 in the Plessy v. Ferguson case. Such decision allowed the proliferation of segregated schools under the belief that, if facilities were equal in quality, such education system was not violating the equality of rights provision that had been guaranteed for all US citizens by the Reconstruction Amendments to the US Constitution.  

Brown v. Board of Education overturned the abovementioned previous Supreme Court decision and declared segregation unconstitutional, claming that, in practice, it actually deprived black students. The court published a deadline and all public schools nationwide had to abolish such practice and to adopt racial integration.

the ones that are losing there jobs

c. the dred scott v. sandford case,