I got it to work...
Thanks to all, you provide the key ideas to get this to work.
You can cut and paste the following code into an IDE.
Hit the go button and the exception thrown depends on the array index
of the exception array.
Change the call to the method from x to y to z to see the effect.
I can now take these ideas and incorporate them into my program.

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;
import java.util.*;

public class MyProgram extends JFrame implements ActionListener
{
  private JButton go   = new JButton ("Go");
  private Container pc = getContentPane();

  Exception [] exceptionFactories = new Exception []
      {
         new IllegalExceptionA(),new IllegalExceptionB (), new
IllegalExceptionC ()
      };

  public void y() throws Exception
  {
     throw exceptionFactories[0];
  }
  public void x() throws Exception
  {
     throw exceptionFactories[1];
  }
  public void z () throws Exception
  {
     throw exceptionFactories [2];
  }
  public static void main (String [] args)
  {
     MyProgram p4 = new MyProgram ();
     p4.setSize(640,480);
     p4.setVisible(true);
     p4.setDefaultCloseOperation (JFrame.EXIT_ON_CLOSE);
  }
  public MyProgram ()
  {
     pc.add (go);
     go.addActionListener (this);
  }
  public void actionPerformed (ActionEvent e)
  {
     try
     {
        x();
     }
     catch (Exception exp)
     {
        System.out.println (exp.toString ());
     }
  }
}

class IllegalExceptionA  extends Exception
{
  IllegalExceptionA  ()
  {
     super ("IllegalExceptionA ");
  }
}
class IllegalExceptionB  extends Exception
{
  IllegalExceptionB  ()
  {
     super ("IllegalExceptionB ");
  }
}
class IllegalExceptionC  extends Exception
{
  IllegalExceptionC  ()
  {
     super ("IllegalExceptionC ");
  }
}