datagridcomboboxcolumn привязка данных

Суть проблемы:

Есть БД

Есть XAML разметка

<Window x:Class="BindingDataWPF.MainWindow"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
    xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
    xmlns:local="clr-namespace:BindingDataWPF"
    mc:Ignorable="d"
    Title="MainWindow" Height="350" Width="525" Loaded="Window_Loaded" Closing="Window_Closing">
<Window.Resources>
</Window.Resources>
<Grid>
    <StackPanel>
        <StackPanel Orientation="Horizontal" VerticalAlignment="Center" HorizontalAlignment="Center" Margin="5">
            <TextBox Name="textBoxName" Margin="5" Width="100" Text="{Binding ElementName=dataGridStudent, Path=SelectedItem.Name, Mode=OneWay}"></TextBox>
            <TextBox Name="textBoxAge" Margin="5" Width="100" Text="{Binding ElementName=dataGridStudent, Path=SelectedItem.Age,  Mode=OneWay}"></TextBox>
            <TextBox Name="textBoxSpec" Margin="5" Width="100" Text="{Binding ElementName=dataGridStudent, Path=SelectedItem.Group.Specialization, Mode=OneWay}"></TextBox>
            <ComboBox Name="comboBoxGroup" Margin="5" Width="100" SelectedItem="{Binding ElementName=dataGridStudent, Path=SelectedItem.Group, Mode=OneWay}" DisplayMemberPath="Number"></ComboBox>
        </StackPanel>
        <StackPanel Orientation="Horizontal" Margin="5" VerticalAlignment="Center" HorizontalAlignment="Center">
            <Button Name="buttonAdd" Margin="5" Click="buttonAdd_Click">Add</Button>
            <Button Name="buttonUpdate" Margin="5" Click="buttonUpdate_Click">Update</Button>
            <Button Name="buttonDelete" Margin="5" Click="buttonDelete_Click">Delete</Button>
        </StackPanel>
        <DataGrid Name="dataGridStudent" Margin="10,10" AutoGenerateColumns="False" CanUserAddRows="False">
            <DataGrid.Columns>
                <DataGridTextColumn Binding="{Binding Id}" ClipboardContentBinding="{x:Null}" Header="ID" Width="Auto"/>
                <DataGridTextColumn Binding="{Binding Name}" ClipboardContentBinding="{x:Null}" Header="Name" Width="*"/>
                <DataGridTextColumn Binding="{Binding Age}" ClipboardContentBinding="{x:Null}" Header="Age" Width="*"/>
                <DataGridTextColumn Binding="{Binding Group.Specialization}" ClipboardContentBinding="{x:Null}" Header="Specialization" Width="*"/>
                <DataGridComboBoxColumn  Header="Group" Width="Auto" ItemsSource="{Binding Group}" DisplayMemberPath="Number">
                </DataGridComboBoxColumn>
            </DataGrid.Columns>
        </DataGrid>
    </StackPanel>
</Grid>

Данные к DataGrid привязываются тут

        private void Window_Loaded(object sender, RoutedEventArgs e)
    {
        db.StudentSet.Load();
        db.GroupSet.Load();
        dataGridStudent.ItemsSource = db.StudentSet.Local.ToBindingList<Student>();
        comboBoxGroup.ItemsSource = db.GroupSet.Local.ToBindingList<Group>();
    }

Ссылка на GitHub

P. S. перелазил весь гугл с этим вопросом, но видимо я слишком не очень чтобы правильно использовать решения, в нем найденные.