Question

Please help meeee!!!!!!!!

Answer 1

`840`

Explanation:

This is a good example of permutations. For the first slot on his shelf, Dylan has 7 trophies to choose from. Then 6, 5, and so on. Since he is only fitting 4 trophies on his shelf, we only continue until we have the slots filled. Thus, we have
`7\cdot 6 \cdot 5\cdot 4=\boxed{840\:\text{ways}}` to do so.

*Note: We do not divide by
`4!` because in this case, order matters. A different order of the same four books still produces different arrangements, so the order matters.