I am arranging my dog's collars on a 6 hanger coat rack on the wall. If she has six collars, how many ways can I arrange the collars on the rack, one per hanger?

720 ways

Step-by-step explanation:

If you are arranging your dog's collars on a 6 hanger coat rack on the wall and if she has six collars, there are 720 ways to arrange them.

Factorial of 6 = 720

For example it could look something like,

Collar 1, Collar 2, Collar 3, Collar 4, Collar 3, Collar 2, Collar 1, and so on.

720 ways to arrange

Step-by-step explanation:

Use the factorial of 6 to find this solution. Namely, 6!

This means 6*5*4*3*2*1 which equals 720

It seems like a huge number, right? But think of it like this: For the first option, you have 6 collars. After you fill the first spot with one of the 6, you have 5 left that will fill the second spot. After the first 2 spots are filled and you used 2 of the 6 collars, there are 4 possibilities that can fill the next spot, etc.