You need to just add ScrollViewer Visibility property to true
Like this :
<ComboBox Name="cmbDepartment" Height="25" Width="200" HorizontalAlignment="Left" Margin="82,34,71,0" ScrollViewer.VerticalScrollBarVisibility="Visible">
<ComboBox.ItemTemplate>
<DataTemplate>
<CheckBox Content="{Binding DepartmentName}" IsChecked="{Binding IsChecked,Mode=TwoWay}" />
</DataTemplate>
</ComboBox.ItemTemplate>
</ComboBox>