Ten horses run in a race. How many different arrangements of placing 1st, 2nd , 3rd?

Question

I tried by doing 10!over 7! But I don't know if that is correct , also how can you tell the finishing number as well.

Answer 1

10 different horses can come in 1st
then 9 different horses come in 2nd, and
then 8 different horse come in 3rd

so number of ways = 10(9)(8) = 720

btw, 10!/7! = 10*9*8*7!/7! = 10*9*8 = 720, which was your answer, so you are right

Answer 2

Yes this is correct thq dear