Five classmates, Barry, Hwan, Daya, Cindy, and Ed will compete in a contest. There are no ties allowed. In how many ways can first, second and third place awards be given out?
(A) 6
(B) 60
(C) 125
(D) 3
(E) 27
The first place award can be given out to any one of the 5 classmates.

Once the first place award has been given, there are 4 classmates remaining who could be awarded second place (since the classmate who was awarded first place cannot also be awarded second place).

For each of the 5 possible first place winners, there are 4 classmates who could be awarded second place, and so there are $5 \times 4$ ways that the first and second place awards can be given out.

Once the first and second place awards have been given, there are 3 classmates remaining who could be awarded the third place award (since the classmates who were awarded first place and second place cannot also be awarded third place).

For each of the 5 possible first place winners, there are 4 classmates who could be awarded second place, and there are 3 classmates who could be awarded third place.

That is, there are $5 \times 4 \times 3=60$ ways that the first, second and third place awards can be given out.

ANSWER: (B)