WPF: Can I bind to a method of the selected object in another control?

I have two WPF list boxes. One is a list of lists (actually a List of ObservableCollection), the other is a list of all known instances of "Thingy".

Here's the datatemplate I'm using for the "thingy" class.

<DataTemplate DataType="{x:Type Model:Thingy}">
    <StackPanel Orientation="Horizontal">
        <CheckBox x:Name="ThingyInListCheckBox" Click="ThingyInList_Click"></CheckBox>
        <TextBlock Text="{Binding Path=ThingyName}"></TextBlock>
     </StackPanel>

Here's the XAML for the list boxes:

<ListBox 
   Name="ListOfGroups"
   SelectionMode="Single">           
</ListBox>
<ListBox 
   Name="ListOfThingys"
   SelectionMode="Single">
</ListBox>

I have the data binding for the list boxes set up in code, because I'm too tired to figure out how to do it in XAML:

ListOfGroups.ItemsSource = InMemoryCache.ThingyGroups;
ListOfThingys.ItemsSource = InMemoryCache.Thingys;

What I want is the checkbox "ThingyInListCheckBox" to be checked if the 'thingy' object is in the list that is the selected item in the "ListOfGroups" listbox. So basically I need to bind it to the "Contains" method of the "ListOfGroups".SelectedItem while passing it the "ListOfThingys".SelectedItem as a parameter.

I'm tempted to do this all in code, but I'm trying to get a better understanding of XAML data binding because I hate myself and I want me to suffer.

Is this even possible, or have I hit the inevitable "wall of databinding" that exists in every other data binding system in the history of software development?

From stackoverflow

• It is possible, in fact the hard thing is that there are many ways to do this and you have to choose one. None of them is a simple addition to your current code. However there is one way, by which you gain more than solving your problem. Actually, it is more of a pattern, called MVVM (some might argue about the naming).

  Here is a small explanation on your example. Suppose ThingyGroup has an IsSelected property, which is bound to the IsSelected property of the containing ListBoxItem. Again, suppose Thingy has a Group property too. Then you can use Group.IsSelected as a path to bind checkbox. Notice that there is still a small issue that IsSelected is a bool and IsChecked is a nullable bool.

  A search on MVVM should give you concrete samples.