You could paint the wall using 6, 5, 4, 3, 2, or only 1 color.
I'm not sure if this is the full question, but if so, we must assume equal probability that you will choose to paint the wall with any particular number of colors.
Probability of painting with 1,2,3,4,5,6 colors = 1/6.
If you used one color, the probability of using white would be 1/6..
2 Colors, 1/6 + 1/5 = 11/30 chance of white being one of the two colors.
...
5 Colors, 1/6 + 1/5 + 1/4 +1/3 + 1/2
..
This will get you a number higher than one, which doesn't make sense. I am either approaching this wrong, or the question is missing something.