How to limit selection of checkboxes, based on selected radiobutton (JAVA FX)

Is it possible to limit the number of checkboxes that can be selected, based on a radiobox that the user selects in the same scne? In my code, there are 2 radiobuttons and 5 color checkboxes. You can only select one radiobutton. If "dog" is selected, I only want the user to be able to select 2 colors. If "cat" is selected, I only want the user to be able to select 3 colors.

    GridPane lay1 = new GridPane();
    lay1.setHgap(0);
    lay1.setVgap(20);

    RadioButton dog = new RadioButton("dog");
    RadioButton cat = new RadioButton("cat");
    ToggleGroup type = new ToggleGroup();
    dog.setToggleGroup(type);
    cat.setToggleGroup(type);
    VBox types = new VBox(20);
    types.getChildren().addAll(dog,cat);
    lay1.add(types, 0, 3);

    CheckBox cb1 = new CheckBox("red");
    CheckBox cb2 = new CheckBox("yellow");
    CheckBox cb3 = new CheckBox("black");
    CheckBox cb4 = new CheckBox("white");
    CheckBox cb5 = new CheckBox("green");

    VBox colors = new VBox(15);
    colors.getChildren().addAll(cb1, cb2, cb3, cb4, cb5);
    lay1.add(colors, 0, 4);`