A good answer might be:

Use a counting loop with a counter from 1 to 1000. The loop body would use a single Random object to pick random X and Y locations for the center of the circles.

Thousands of Circles

Here is a start on this idea: 

// assume that the drawing area is 400 by 400
public class ThousandCircles extends Applet
{
  Circle circ = new Circle();
  Random rand = _________________;
  
  public void paint ( Graphics gr )
  { 

    circ.setRadius(  5 );
    circ.setColor( Color.red );
    int count = 1;
    while ( count <= 1000 )
    {

      int x = _________________;
      int y = _________________;

      circ.setPosition( x, y );
      circ.draw( gr );

      count = count + 1;
    }
  }
}

To make sure that each circle completely fits within the applet drawing area, make sure that each center's x and y is at least a distance of 5 (the radius) away from an edge. But let us not do that.

QUESTION 16:

Complete the applet by filling in the blanks. The drawing area is going to be 400 by 400.