drawing names from ahat ..dont understand it
I also knew that the senior officers in the company had
spent much. time considering which one of the four would be
promoted. My three disillusioned friends should have realized
that top executives don't select major executives by drawing
names from a hat.

Question

drawing names from ahat ..dont understand it
I also knew that the senior officers in the company had 
spent much. time considering which one of the four would be 
promoted. My three disillusioned friends should have realized 
that top executives don't select major executives by drawing 
names from a hat.

Answer

It means 'randomly choosing'.
The idea is that you write people's names on a piece of paper, and put all the papers in a hat (or some other container), someone pulls out a piece of paper, and the person whose name is written on it is selected.
It's a reasonably common way of randomly choosing between a few alternatives.