Generating Random Graphics + Questions About Learning Java

Before anything: Is it alright to submit a question to Stack Overflow when you're trying to learn to code? I've really put about 20 hours into this problem and am entirely stuck, but if I should remain stuck for the experience of realizing how to craft my own solutions, please say the word Stack Overlords.

I am attempting to create a function that creates ten circles of a semi-random size and location and a random color.

The size and location are semi-random because the circle's radius must be between 5 - 50 pixels; the location must be within the Jpanel.

The color can be anything. The production of the circles must stop at ten and all the circles must be static in the same Jpanel at once.

I've finished the problem almost entirely asides from being able to get the ten circles to remain static within the Jpanel after they've been generated.

I've tried applying a basic for-loop around various sections of the code I thought could produce the desired result. My for-loop is shown below.

for(int i = 0; i < 10; ++i) { }

package assignment3;
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.Random;
import javax.swing.JFrame;

public class Random_Circles extends JPanel{

private static final long serialVersionUID = 1L;

// Below is the input for our random size.
    public static int RandomSize() {
        double randomDouble = Math.random();
        randomDouble = randomDouble * 50 + 1;
        int randomInt = (int) randomDouble;
        return randomInt;
    }

// Below is the input for our random X-coordinate.
    public static int RandomPosition1() {
        double randomDouble = Math.random();
        randomDouble = randomDouble * 900 + 1;
        int randomInt = (int) randomDouble;
        return randomInt;
    }

// Below is the input for our random Y-coordinate.
    public static int RandomPosition2() {
        double randomDouble = Math.random();
        randomDouble = randomDouble * 400 + 1;
        int randomInt = (int) randomDouble;
        return randomInt;
    }
// I don't really know what this does, but I've gotta do it apparently. 
    Random rand = new Random();

// Below is the input for our random color.
    public void paintComponent(Graphics RC) {
        super.paintComponent(RC);
        this.setBackground(Color.white); 

        // Random Size  
        int RS; 
        RS = RandomSize();

        // X-coordinate
        int RP1;
        RP1 = RandomPosition1();

        // Y-coordinate
        int RP2;
        RP2 = RandomPosition2();

        // Color inputs
        float r = rand.nextFloat();
        float g = rand.nextFloat();
        float b = rand.nextFloat();
        Color randomColor = new Color(r, g, b);

        // Color function
        RC.setColor(randomColor);

        // Location and size function 
        RC.fillOval(RP1, RP2, RS, RS);
        }
}



///Main function that produces Jpanel, calls previous code.

package assignment3;
import javax.swing.JFrame;

import assignment3.Random_Circles;

public class Random_Circles_Exe {

        public static void main(String[] args) {
            JFrame f = new JFrame("Random Cirlces");
            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            Random_Circles r = new Random_Circles();
            f.add(r);
            f.setSize(1000,500);
            f.setVisible(true);
            }
        }

Expected: Ten circles with the required parameters appearing and remaining in the JPanel.

Actual: Ten circles being generated the second the function runs, but with each new circle the old one expires. With re-sizing the Jpanel ( just by clicking and dragging its border ), more circles are generated.