<dg:DataGrid Name="gridList" AutoGenerateColumns="False"
ItemsSource="{Binding ItemsInTable}" HeadersVisibility="Column" >
<dg:DataGrid.RowDetailsTemplate >
<DataTemplate x:Name="ItemDetails" >
<Border HorizontalAlignment="Stretch" CornerRadius="5" Background="Azure" >
<StackPanel Orientation="Vertical" Margin="0,10,0,0">
<ComboBox Name="cboxDepartment" SelectedItem="{Binding Department}" DisplayMemberPath="Desc" ItemsSource="{Binding DeptosInTable}" ></ComboBox>
</StacPanel>
</Border>
</DataTemplate>
</dg:DataGrid.RowDetailsTemplate>
<dg:DataGridTextColumn Header="DEPARTMENT" Binding="{Binding Department}" Width="180" IsReadOnly="True">
Department is a property in a class. DeptosInTable is a ObservableCollection with 2 properties: ID and Desc.