By Lawrence Crook III, Jean Casarez, and Ellie Kaufman

CNN

(CNN) -- Eleven jurors have been picked thus far for the Bill Cosby trial after the second day of jury selection at the Allegheny County Courthouse in Pennsylvania. Cosby faces sexual offense charges that could land the former comedian in prison.

Seven jurors are white men, three are white women and there is one black woman.

The full jury will include 12 jurors and six alternates. They will be bused and sequestered in a hotel for the length of the trial, which is expected to last two or three weeks. The trial is set to begin June 5 in Montgomery County, north of Philadelphia.

"We made a lot of progress today," Cosby defense attorney Brian McMonagle said Tuesday outside of the courthouse. "We're looking to finish the process tomorrow, and we are hopeful that we'll be able to do so."

Cosby, 79, is charged with three counts of felony aggravated indecent assault from a 2004 case involving Andrea Constand, an employee at his alma mater, Temple University. He has pleaded not guilty to all charges.

Constand was the first of more than 50 women who accused Cosby of sexual misconduct, but this is the only criminal trial Cosby has faced. Many allege he drugged and sexually assaulted them.

The prosecution on Tuesday used its fourth of seven preemptive strikes to block a black woman from the jury. The woman, a former Pittsburgh police officer, had previously been arrested and charged with falsifying records, according to prosecutors.

Charges were ultimately dismissed, as was a subsequent civil lawsuit brought by the woman and others against the city of Pittsburgh. Those past legal issues allowed prosecutors to argue that the juror could have credibility issues, as well as bias against the commonwealth.

McMonagle challenged the prosecution's move, arguing that it was a violation of U.S. Supreme Court ruling Batson vs. Kentucky, which states prosecutors must find a race-neutral reason for keeping minorities off juries with a preemptive strike.

The judge ruled in favor of the prosecution, allowing them to block the woman's appointment, unless the defense can prove that the prosecution did so for racial reasons.

"There has been a systemic exclusion of African-Americans," McMonagle said in court.

Cosby does not plan to testify in his own defense, he told CNN host Michael Smerconish last week.

If convicted, he faces up to 30 years in prison.

Judge Steven O'Neill denied a request to move the trial from Montgomery County, which Cosby had sought due to pretrial publicity.

Cosby, who has been present in court for the selection of his jury, is always escorted by a member of his team. Cosby is "legally unsighted" due to problems linked to glaucoma, he told Smerconish. He has declined to answer questions as he's come and gone from court.

CNN's Jay Croft contributed to this report.