# Combination

• Nov 24th 2008, 05:15 PM
Linnus
Combination
There are 6 windows and you want to paint them. There are 4 colors to choose from, but you cannot mix the colors the windows. (each window must have a unique color)
How many different combinations can you paint the windows?

I think the answer is 3 x 4! or 6 x 4! but something doesn't feel right
• Nov 24th 2008, 05:48 PM
Paint the windows one at a time. There are 4 colours you can paint the first window, and 4 you can paint the second, and the third etc. so the number of combinations is $4^6$ by the multiplication principle.
• Nov 24th 2008, 05:50 PM
Linnus
Quote:

Paint the windows one at a time. There are 4 colours you can paint the first window, and 4 you can paint the second, and the third etc. so the number of combinations is $4^6$ by the multiplication principle.

Hmm...Each window must have a unique color.
• Nov 24th 2008, 06:22 PM
Quote:

Hmm...Each window must have a unique color.
I think the answer is 0 then, because there are 6 windows and only 4 colours. If you want to seem extra mathy, invoke the pigeonhole principle.