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In 2007, the court struck down a Seattle policy that used skin color to divide elementary students equally throughout the city’s school system. In the majority opinion, Chief Justice John G. Roberts Jr. called the schools’ methods “extreme.”

“The way to stop discriminating on the basis of race is to stop discriminating on the basis of race,” he wrote.

Liberal-leaning Justice Elena Kagan, who as the Obama administration’s solicitor-general worked on the Fisher case at the lower-court level, has recused herself. Some analysts think her absence makes the outcome of the case all but certain.

“The justices will have the opportunity to revisit and likely narrow the circumstances under which the universities can use race-sensitive measures,” Ms. Brown-Nagin said.

Another potential indicator of how the court may rule is the 2009 New Haven firefighters case, in which the justices said the Connecticut city had violated the civil rights of 20 firefighters by throwing out the results of a promotion exam because not enough blacks had passed it.

Much like Ms. Fisher’s contention, the firefighters - 19 of them white and one Hispanic - argued that they were harmed by policies designed to help certain racial groups.

Arguments in the Fisher case are likely to begin in October. It’s the latest addition to an already packed Supreme Court docket, highlighted by the widely anticipated case of President Obama’s health care initiative.