How to set an item as selected in a combobox

Not sure why you can't data bind to SelectedItem on a ComboBox without seeing your code. Below shows you how to do it using a CollectionView which has current item management built in which comboboxes supports. CollectionView has a CurrentItem get property you can use to get currently selected.

XAML:

<Window x:Class="CBTest.Window1"
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    Title="Window1" Height="300" Width="300">
    <StackPanel>
        <ComboBox 
            ItemsSource="{Binding Path=Names}"
            IsSynchronizedWithCurrentItem="True">
            <ComboBox.ItemTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding}" />
                </DataTemplate>
            </ComboBox.ItemTemplate>
        </ComboBox>
        <TextBlock Text="{Binding Path=Names.CurrentItem}" />
    </StackPanel>
</Window>

Code behind:

using System.Collections.Generic;
using System.Windows;
using System.Windows.Data;

namespace CBTest
{
    public partial class Window1 : Window
    {
        public Window1()
        {
            InitializeComponent();

            DataContext = new VM();
        }
    }

    public class VM
    {
        public VM()
        {
            _namesModel.Add("Bob");
            _namesModel.Add("Joe"); 
            _namesModel.Add("Sally"); 
            _namesModel.Add("Lucy");

            Names = new CollectionView(_namesModel);

            // Set currently selected item to Sally.

            Names.MoveCurrentTo("Sally");
        }

        public CollectionView Names { get; private set; }

        private List<string> _namesModel = new List<string>();
    }
}

Our successful approach for binding a combobox is the following...

<ComboBox 
    ItemsSource="{Binding Path=AllItems}" 
    SelectedItem="{Binding Path=CurrentItem, Mode=TwoWay}" />
<TextBlock Text="{Binding Path=CurrentItem, Mode=TwoWay}" />

class public ItemListViewModel
{
    public ObservableCollection<Item> AllItems {get; set;}

    private Item _currentItem;
    public Item CurrentItem
    {
        get { return _currentItem; }
        set
        {
            if (_currentItem == value) return;
            _currentItem = value;
            RaisePropertyChanged("CurrentItem");
        }
    }
}