we know that
There are: 9 ways to put the first trophy.
8 ways to put the second trophy after putting the first one.
7 ways to put the third trophy after putting the second one.
6 ways .............the third one
5 ways --------> the fourth
4 ways------> 5
3 ways -----> 6
2 ways ----> 7
1 ways-----> 8
therefore
n!
where n=9
9!=9*8*7*6*5*4*4*2*1
9!=362,880
the answer is
362,880 ways