remove array from random when used

I'm not certain if the title is the right way to word what I'm asking, sorry if it's not, but what I'm trying to do is create a memory match game using GUI. I have an array, and I've got the button printing an element from the array at random, but, the issue is, that I can have the same element printing multiple times. Is there a way to remove that element from being selected once it's used? If there isn't a way to do that, any ideas on how I could go about getting it to use each element only once? This is my current code:

    package MemoryMatching;
import java.awt.BorderLayout;
import java.awt.GridLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

import java.util.Random;

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;

public class MemoryGUI extends JFrame implements MemoryMatch, ActionListener{
    JPanel mainPanel, boardPanel;
    JButton [][] gridButtons = new JButton[3][4];
    char cardArray[] = new char[12];
    int numInPlay;

    public MemoryGUI(){
        cardArray[0] = 'A';
        cardArray[1] = 'A';
        cardArray[2] = 'B';
        cardArray[3] = 'B';
        cardArray[4] = 'C';
        cardArray[5] = 'C';
        cardArray[6] = 'D';
        cardArray[7] = 'D';
        cardArray[8] = 'E';
        cardArray[9] = 'E';
        cardArray[10] = 'F';
        cardArray[11] = 'F';
        mainPanel = new JPanel();
        mainPanel.setLayout(new BorderLayout());
        boardPanel = new JPanel();
        boardPanel.setLayout(new GridLayout(4,3));
        setBoard();
        mainPanel.add(boardPanel, BorderLayout.CENTER);
        add(mainPanel);
    }
    @Override
    public void actionPerformed(ActionEvent e) {
        JButton btnClicked = (JButton) e.getSource();
        btnClicked.setEnabled(false);
        char randomChar = cardArray[(int)new Random().nextInt(cardArray.length)];

        btnClicked.setText(""+ randomChar);
        faceUp();

    }

    @Override
    public void setBoard() {
        for(int x = 0; x < cardArray.length; x++) {

        }
        for(int row=0; row<gridButtons.length; row++){
            for(int col=0; col<gridButtons[row].length;col++){
                gridButtons[row][col] = new JButton();
                gridButtons[row][col].addActionListener(this);
                gridButtons[row][col].setText("No peeking");
                boardPanel.add(gridButtons[row][col] );
                faceDown();
            }
        }
    }

    @Override
    public void isWinner() {
        // TODO Auto-generated method stub

    }
    @Override
    public void isMatch() {


    }
    @Override
    public void faceUp() {
        for(int x = 0; x < cardArray.length; x++) {
            for(int y = 0; y < cardArray[x]; y++) {

            }
        }
    }
    @Override
    public void faceDown() {


    }
}

what I'm currently getting is something like A B A A F B F D D E F C rather than: B A C D E F A B C F E D The first example having three A and one C, rather than two of each as in the second example. If possible I'd like to not be given the code outright, but a push towards the right direction.