OK. I figured out how to place/color it randomly, but now I need to figure out how to put it all inside a box. It is randomly placed throughout the whole screen, and I don't really know how to box it in. Here's what I have now.
Random rndInt = new Random(1234);
for (int k = 1; k <= 100; k++)
{
int x = rndInt.nextInt(800);
int y = rndInt.nextInt(600);
int red = rndInt.nextInt(256);
int green = rndInt.nextInt(256);
int blue = rndInt.nextInt(256);
g.setColor(new Color(red,green,blue));
g.fillOval(x,y,50,50);
}