C# calling the same function with ListBox or ComboBox

I have series of listboxes and comboboxes that I want to update, so that the items listed are the same as those listed in a IEnumerable<string>. I do understand that data binding might help, but I think it could be a bit of a struggle now, and I'd rather avoid it. I wrote something like this:

    public static void UpdateListboxWithStrings(
        ListControl listcontrol, 
        IEnumerable<string> stringlist)
    {
        Object listcontrolitems;
        if (listcontrol is ListBox)
        {
            listcontrolitems =
                ((ListBox)listcontrol).Items;
        }
        else if (listcontrol is ComboBox)
        {
            listcontrolitems =
                ((ComboBox)listcontrol).Items;
        }
        else
        {
            //// Wrong control type.
            //// EARLY EXIT
            return;
        }
        int itemscount = listcontrolitems.Count;
        /// More code here...
    }

... And troubles begin. Depending on what I add / remove, listcontrolitems appears undefined, or must be initialized, or it doesn't have properties such as Count.

How do you write a function that works with a combobox or in a listbox without code duplication?