WPF DataGridComboBoxColumn Edit on Key press

Question

I have a datagrid with a DataGridComboBoxColumn in it.

I want my users to be able to enter edit mode by just typing.
This is the default behavior for DataGridTextColumn and I don't like that they have to press F2 in order to enable editing for just this column type.

How can I make the DataGridComboBoxColumn enter edit mode without them needing to press F2? Ideally on Key Press, but I would be fine if it entered edit mode on focus as well.

Solution Modifications to the accepted answer that bring back the basic functionality of the datagrid:

 void Cell_PreviewKeyDown(object sender, KeyEventArgs e)
    {
        if(e.Key == Key.Enter || e.Key == Key.Tab)
        {
            dgBins.CommitEdit();
            dgBins.SelectedIndex += 1;
        }else if(e.Key.ToString().Length == 1 
            || (e.Key.ToString().StartsWith("D") && e.Key.ToString().Length == 2)
            || e.Key.ToString().StartsWith("NumPad")
            || e.Key == Key.Delete 
            || e.Key == Key.Back )
        { 
            if (e.OriginalSource is DataGridCell)
            {
                DataGridCell cell = (sender as DataGridCell);
                Control elem = FindChild<Control>(cell, null);
                elem.Focus();
            }
        }
    }

Answer 1

    <DataGrid.CellStyle>
         <Style TargetType="DataGridCell">
             <EventSetter Event="PreviewKeyDown" Handler="Cell_PreviewKeyDown"/>
             <EventSetter Event="GotFocus" Handler="Cell_GotFocus"/>
         </Style>
    </DataGrid.CellStyle>

Handlers :

void Cell_PreviewKeyDown(object sender, KeyEventArgs e)
{
    if (e.OriginalSource is DataGridCell)
    {
        DataGridCell cell = (sender as DataGridCell);
        Control elem = FindChild<Control>(cell, null);
        elem.Focus();
    }
}

void Cell_GotFocus(object sender, RoutedEventArgs e)
{
    DataGridCell cell = (sender as DataGridCell);
    cell.IsEditing = true;
}

Helper :

public static T FindChild<T>(DependencyObject parent, string childName)
        where T : DependencyObject
{
    // Confirm parent and childName are valid. 
    if (parent == null) return null;

    T foundChild = null;

    int childrenCount = VisualTreeHelper.GetChildrenCount(parent);
    for (int i = 0; i < childrenCount; i++)
    {
        var child = VisualTreeHelper.GetChild(parent, i);
        // If the child is not of the request child type child
        T childType = child as T;
        if (childType == null)
        {
            // recursively drill down the tree
            foundChild = FindChild<T>(child, childName);

            // If the child is found, break so we do not overwrite the found child. 
            if (foundChild != null) break;
        }
        else if (!string.IsNullOrEmpty(childName))
        {
            var frameworkElement = child as FrameworkElement;
            // If the child's name is set for search
            if (frameworkElement != null && frameworkElement.Name == childName)
            {
                // if the child's name is of the request name
                foundChild = (T)child;
                break;
            }
        }
        else
        {
            // child element found.
            foundChild = (T)child;
            break;
        }
    }

    return foundChild;
}

If this solves your problem.