I think the question I'm asking is similar to How to populate a DataGridComboBoxColumn? but mine is from a DataTable instead of a class. I've created a dataset to use as an example. But basically, the column is blank when I load it, but when I select an item from the combo box, it still edits the datatable as expected, but I think I'm missing something to bind the data to the column.
        DataTable dt;
        public MainWindow()
        {
            InitializeComponent();
            CreateDT();
        }
        public void CreateDT()
        {
            dt = new DataTable();
            dt.Columns.Add("Name", typeof(string));
            dt.Columns.Add("Position", typeof(string));
            // List for the options in the comboBox
            List<string> list = new List<string>()
            {
                "Position 1",
                "Position 2",
                "Position 3",
                "Position 4",
                "Position 5"
            };
            // datatable
            for (int i = 0; i < 10; i++)
            {
                dt.Rows.Add("Person A", "Position A");
            }
            ComboBoxColumn.ItemsSource = list;
            RestoreTable.ItemsSource = dt.DefaultView;
        }
        private void Button_Click(object sender, RoutedEventArgs e)
        {
            // Adding a break point here so I can debug what the datatable looks like after selecting a value
        } 
With the XAML for it
    <Grid>
        <DataGrid Name="RestoreTable" AutoGenerateColumns="False" HorizontalAlignment="Center" VerticalAlignment="Top" CanUserAddRows="False">
            <DataGrid.Columns>
                <DataGridTextColumn Header="Name" Binding="{Binding Name}"/>
                <DataGridComboBoxColumn x:Name="ComboBoxColumn" 
                                        Header="Position" 
                                        SelectedItemBinding="{Binding List}" 
                                        SelectedValueBinding="{Binding Position}"
                                        ???????/>
            </DataGrid.Columns>
        </DataGrid>
        <Button Content="Button" HorizontalAlignment="Left" Margin="703,352,0,0" VerticalAlignment="Top" Width="75" Click="Button_Click"/>
    </Grid>
