# Three different medals- gold, silver and bronze- are awarded to athletes in TWO different races...

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!

I think the text is trying to say that no athlete can win two medals in both races, thus every participant (since there’s $$6$$ of them and $$6$$ medals) must win one and only one medal.
So the answer is just the number of ways you gan give these $$6$$ medals to the $$6$$ racers, or simply $$6!$$