.
10*9*8 ways.
You can choose the first winner by 10 ways;
then you can choose the second winner by 9 ways among remaining 9 people.
Finally, you can choose the third winner by 8 ways anong remaining 8 people.
It gives you the final answer 10*9*8 ways.
It is a STANDARD way to solve such problems.
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Comment from student: So, is that the answer ; or do you supposed to multiply 10*9*8 which equals to “720”? Thanks.
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My response: Hey, I assume that after receiving the formula from me you are able to calculate the number.