TwoWay Binding of a ComboBox to a static property

Question

-------EDIT------

So, i figured that my code is correct and so are the code snippets from all of your answers. Thanks for that. My

Answer 1

Checked just in a sample project, works fine

public class ViewModel
{
    static ViewModel()
    {
        Items=new ObservableCollection();
        SelectedItem = "222";
        Items.Add("111");
        Items.Add("222");
        Items.Add("333");
        Items.Add("444");
        Items.Add("555");
    }
    private static string _selectedItem;
    public static string SelectedItem
    {
        get { return _selectedItem; }
        set { _selectedItem = value;
            MessageBox.Show("Item " + value + " was selected");
        }
    }

    private static ObservableCollection _items;
    public static ObservableCollection Items
    {
        get { return _items; }
        set { _items = value; }
    }
}

and xaml

I have uploaded sample.