Answer :

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