if you mean the wpf toolkit datagrid, you could do it like so:
<dg:DataGridComboBoxColumn
Header="String Column"
SelectedItemBinding="{Binding Path=RoleProperty}">
<dg:DataGridComboBoxColumn.ItemsSource>
<CompositeCollection>
<system:String>Employee</system:String>
<system:String>Contractor</system:String>
<system:String>Supplier</system:String>
</CompositeCollection>
</dg:DataGridComboBoxColumn.ItemsSource>
</dg:DataGridComboBoxColumn>
in this the items displayed have a property called RoleProperty. you would also need an xnl namespace defintion at the top of your xaml (with the rest of them like:
xmlns:system="clr-namespace:System;assembly=mscorlib"
to let you include the system namespace. (to get access to the Strings)