In a race with 5 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 from the following options:
A) 35
B) 120
C) 720
D) 840
E) 60
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 5 choices ,for silver 4 remain (one who got gold cannot be given silver) and for bronze 3 choices remain.   So total possibilities=5*4*3   Correct answer 60=60
<result>E</result>
In a race with 5 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?