Using the permutation formula, it is found that there are 840 possible arrangements of the 4 trophies.
The problem says the word "arrangements", which implies that the order matters, hence the permutation formula is used to solve this question.
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 4 elements from a set of 7 are arranged, hence:
[tex]P_{7,4} = \frac{7!}{3!} = 840[/tex]
There are 840 possible arrangements of the 4 trophies.
More can be learned about the permutation formula at https://brainly.com/question/25925367
