# How many options are there to award gold, silver, and bronze medals to a group of $10$ athletes?

How many options are there to award gold, silver, and bronze medals to a group of $10$ athletes?

Is this permutation or combination, and is there repetition? I thought this would be a combination without repetition, where I found the formula to be: $\frac{n!}{(n-r)!} = \frac{10!}{7!} = 720$ I'm doubting that this is correct though. Did I do something wrong?

• This is a permutation, and your answer is right. There are 10 choices for the gold, then 9 choices for the silver, and 8 possibilities for the bronze, giving $10\cdot9\cdot8=720$ – user84413 Feb 4 '16 at 17:15