Although it might seem frustrating to those at the scene of some frightful event causing the emergency not to rush to the injured first, it is vital to ensure that the scene is safe to enter first. It helps no-one to rush in in a foolhardy manner if there are hazards that could hamper any help you might give.
After securing the area to protect further people from entering somewhere dangerous, the most seriously injured must be tended to first, having checked for signs of life in all affected people. The emergency services must be contacted next while you attend and perhaps need to give life-saving attention, such as mouth-to-mouth resuscitation.