Three different medals- Gold, Silver and Bronze- are awarded to athletes in two different races. If no athlete may win more than one medal, and there are 6 athletes in total, how many different combinations are there?
I know that the first race: $6\cdot 5\cdot 4= 120$
I feel like the answer for both races should be $120+120= 240$.
But this is not an answer choice so I must be wrong!