In a race with 5 runners, in how many different ways can 1st, 2nd, and 3rd place be awarded?

The order matters because 1st, 2nd, and 3rd place are different awards. There are $5$ choices for first place, then $4$ for second, then $3$ for third, so the total is $5\cdot4\cdot3=60$, choice H. This is the permutation $P(5,3)$. Choice F ($10$) is the combination $C(5,3)$, which counts groups of three runners without regard to order. Choice G ($15$) is $5\cdot3$, which uses only two of the three positions. Choice J ($125$) is $5^3$, which would let the same runner win all three places.