How to bind a combobox inside wpf datagrid?

How to bind (Itemssource and selected item) of a combobox inside wpf datagrid? I am using MVVM pattern. I have tried

<DataGridTemplateColumn Header="Example 9">
                        <DataGridTemplateColumn.CellTemplate>
                            <DataTemplate>
                                <ComboBox ItemsSource="{Binding PartIds, RelativeSource={RelativeSource AncestorType=Window}}" SelectedItem="{Binding PartId, UpdateSourceTrigger=PropertyChanged}" />
                            </DataTemplate>
                        </DataGridTemplateColumn.CellTemplate>
                    </DataGridTemplateColumn>

and

   <DataGrid AutoGenerateColumns="False" ItemsSource="{Binding MyCars}" HorizontalAlignment="Left">
                <DataGrid.Columns>
                    <DataGridTextColumn Header="Model" Binding="{Binding Model}"/>
                    <DataGridTextColumn Header="Registration" Binding="{Binding Registration}"/>

                    <DataGridTemplateColumn Header="Example 12">
                        <DataGridTemplateColumn.CellTemplate>
                            <DataTemplate>
                                <ComboBox ItemsSource="{Binding CarParts, RelativeSource={RelativeSource AncestorType=Window}}" DisplayMemberPath="PartName" SelectedValuePath="PartID"  SelectedValue="{Binding PartId, UpdateSourceTrigger=PropertyChanged}" />
                            </DataTemplate>
                        </DataGridTemplateColumn.CellTemplate>
                    </DataGridTemplateColumn>

                    <DataGridTextColumn Header="Selected" Binding="{Binding PartId}"/>

                </DataGrid.Columns>
            </DataGrid>

Properties used for data-binding

#region DataGrid List<String> Example

        public ObservableCollection<MyCar> MyCars { get; set; }
        public List<string> PartIds { get; set; } 

        #endregion

        #region DataGrid List<Class> Example

        public List<CarPart> CarParts { get; set; }

        #endregion

Reference: http://code.msdn.microsoft.com/windowsdesktop/Best-ComboBox-Tutorial-5cc27f82