In a race with 20 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded? Choose the correct choice.
A) 35	B) 120	C) 720	D) 840	E) 6,840
Well in this case since there are 3 positions and they can be taken by 3 persons only ,so order matters over here .For gold there are 20 choices ,for silver 19 remain (one who got gold cannot be given silver) and for bronze 18 choices remain.   So total possibilities=20*19*18   Correct answer 6,840=6,840
<result>E</result>
In a race with 20 competitors, the first-place finisher receives a gold medal, the second-place finisher receives a silver medal, and the third-place finisher receives a bronze medal. If there are no ties, in how many different ways may these three medals be awarded?