He went to University of Memphis, where he earned Conference USA Rookie of the Year and freshman All-American honors on averages of 15.4 points per game and a team-best 3.8 assists. With no time remaining in the championship game of the 2005 Conference-USA tournament, Washington was given three free throws to overcome a 75-73 lead by the sixth-ranked Louisville Cardinals. Although Washington was a 72-percent shooter, he missed two of the three foul shots, giving Louisville the win and an appearance in the NCAA Tournament while Washington and the Tigers' season would continue in the NIT, where they would reach the semifinal round.