Question

Hello! I am needing some reassurance please. Just the top question.

Answer 1

840

Step-by-step explanation

Lauren has 7 trophies and wants to know how many possible arrangements with 4 trophies there are. If we want to know how many different arrangements, then order matters so we would use a permutation.

But we can also think it logically and we will get the same answer if we do it right. Let's see, for the first shelf space, there are 7 trophies available to pick from. Then for the second shelf space, there are 6 trophies left. Then, for the third space, there are 5 trophies left and, finally, for the fourth space there are 4 trophies to pick from,

`7\cdot6\cdot5\cdot4=840`

If we do it with a permutation,

`_7P_4=(7!)/((7-4)!)=(7!)/(3!)=(7\cdot6\cdot5\cdot4\cdot3!)/(3!)=7\cdot6\cdot5\cdot4=840`

Hence, there are 840 possible arrangements.