Answered

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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?

Sagot :

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

Now, we need to use the permutation formula:

[tex]P(n,r)=\frac{n!}{(n-r)!}[/tex]

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

the number of doors.

Replacing on the permutation formula:

[tex]P(10,3)=\frac{10!}{(10-3)!}[/tex][tex]P(10,3)=\frac{10!}{7!}[/tex][tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=10x9x8![/tex]

Then

[tex]P(10,3)=\frac{10x9x8x7!}{7!}[/tex][tex]P(10,3)=720[/tex]

Hence, there are 720 possible arrangements for the doors.

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