 Allums attended Lynwood High School, where his 18 points and 18 rebounds per game helped lead his team to the Southern Section 3A championship.A 6'9" forward playing on scholarship for the UCLA Bruins men's basketball team, Allums played for three different coaches and ended his collegiate career by playing four minutes in UCLA's loss to the University of Louisville in the finals of the 1980 NCAA Men's Division I Basketball Tournament.Allums was selected with the 11th pick in the fifth round of the 1980 NBA Draft by the Dallas Mavericks and played one season (1980-81) for them, averaging 2.7 points, 3.0 rebounds and 1.1 assist per game.