Answer:
720 different ways
Step-by-step explanation:
To decide whether you are doing a Permutation or Combination, ask yourself if order matters. If the order of things is important then it is a permutation question, if the order doesn't matter then it is a combination question.
In this case, the order is important because there is a difference who will be the first place winner, the second place winne and the third place winner.
Use permutation formula:
[tex]P^{10}_3=\dfrac{10!}{(10-3)!}=\dfrac{10!}{7!}=\dfrac{7!\cdot 8\cdot 9\cdot 10}{7!}=8\cdot 9\cdot 10=720[/tex]
