[color=#000000]Fifty-seven students participated in a lottery for a particularly desirable dorm room – a triple with a fireplace and private bath in the tower. Twenty of the participants were members of the same varsity team. When all three winners were members of the team, the other students complained. Describe a simulation to determine whether an all-team outcome could reasonably be expected to happen if everyone had a fair shot at the room. [br][br]In the applet below, each dot represents the number of varsity players selected without replacement out of 3 people selected. There are 100 simulated trials.[/color]