Open the DropDown When the Control Gets Focus
RadComboBox's API gives you the ability to open the DropDown when the control gets focus. In order to enable this behavior you should set the RadComboBox's OpenDropDownOnFocus property to True.
<telerik:RadComboBox x:Name="radComboBox" OpenDropDownOnFocus="True"/>
The default value of the RadComboBox's OpenDropDownOnFocus property is False.