You are hanging 6 pictures next to one another on your wall. How many different arrangements are there?

Question

You are hanging 6 pictures next to one another on your wall. How many different arrangements are there?

Answer 1

If you have n objects there are n! permutations of these objects.

If you have n objects and select r of them you have n! / (n - r)! permutations of the r objects.  This can be written as n P r.

here we have 6 P 6 = 6! = 720

Answer 2

There are 720 different combinations. If you multiply 6x5x4x3x2x1, your answer will be 720. If you want to know any combination of different things, just follow this type of multiplication until 1.

Answer 3

This is all just combinatorics! Easy peasy!

You have 6 choices for first position.

Followed by 5 for the next.

And so on....

Answer: 6 * 5 * 4 * 3 * 2 * 1 = 720 ways to arrange the pictures.