Explain how these three sentences differ in meaning.?

exhibited is more formal, while it does mean showed i would be inclined not to use it, because it sounds too formal. The verb flaunted is better, because it is more descriptive of her manner, saying that she is showing off the the crowd, and that she is arrogant. Showed is the most basic, and literal word. I would go for flaunted, providing of course that she was actually flaunting the ribbon, not just showing it.