Question

In the front of a building there are three doors each to be painted

a different color from 10 different available colors. How many color
arrangements for the doors are there?

Answer 1

In this case, the order doesn't matter and the colors cant be repeated.

Now, we need to use the permutation formula:

`P(n,r)=(n!)/((n-r)!)`

Where n represents the total different available colors and r is equal to

the number of doors.

Replacing on the permutation formula:

`P(10,3)=(10!)/((10-3)!)`
`P(10,3)=(10!)/(7!)`
`P(10,3)=(10x9x8x7!)/(7!)`
`P(10,3)=10x9x8!`

Then

`P(10,3)=(10x9x8x7!)/(7!)`
`P(10,3)=720`

Hence, there are 720 possible arrangements for the doors.