In a race with 10 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?
Answer choices:
35
120
720
840
604,800
I'm sure this is a basic combinatorics question, but I'm curious to know something: could you show me the combinatorics for three medalists, as well as for ten medals, if they were to be awarded to all runners?
Thanks in advance,
Kelsey