[2010] Adding ComboBox to ListView and binding to the selected value

I need to add a ComboBox to a ListView to display possible values of an Enum and bind the selected item to the value of a variable of that Enum. Unfortunately, my attempts are failing miserably and Google isn't helping much either.

Here's my code, I would appreciate it if you could take a look and tell me what I'm doing wrong.

Code:

---

<GridViewColumn Header="  Data  " Width="Auto">
    <GridViewColumn.CellTemplate>
        <DataTemplate>
            <ComboBox Margin="0" MinWidth="50" SelectedItem="{Binding Mode=TwoWay, Path=ColumnType}" Width="Auto" HorizontalAlignment="Stretch" VerticalAlignment="Stretch">
                <TextBlock>Integer</TextBlock>
                <TextBlock>Double</TextBlock>
            </ComboBox>
        </DataTemplate>
    </GridViewColumn.CellTemplate>
</GridViewColumn>

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Also, the class I'm binding the controls to looks like this:

Code:

---

private class ListViewItemBinder
{
    public CustomEnum ColumnType {get; set; }
}

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I considered alternatives such as using the SelectedIndexChanged event etc, but that doesn't provide a way to set the initial value of the ComboBox...

Any help would be greatly appreciated.