Question

You are choosing 4 of your 7 trophies and arranging them in a row on a shelfIn how many different ways can you choose and arrange the trophies?A. 840B. 28C. 24D. 5040

Answer 1

The formula to find how many different ways are there to choose a subgroup of r things from a group of n things is

$\frac{n!}{(n-r)!}$

Here, you have 7 trophies and you want to choose 4 of them, so you have

$\frac{7!}{(7-4)!}\text{ = }\frac{5040}{6}=840$

So there are 840 ways to choose your 4 trophies out of the 7 you have.