See this thread http://www.gmatclub.com/phpbb/viewtopic.php?t=14706
Once you identify that this is binomial distribution case, you should simply use the formula.
P = (0.9^4) * (0.1^1) * C(5,4) = 32.8%
Narrative: I assume you just multiplied 0.9 four times to reach the answer. That's not enough, because this way you can't be sure about the voting status of the 5th person. So you plug in his 10% probability, and you get (0.9^4) * (0.1^1) ~ 0.066. But this is incomplete, because we haven't considered if the 10% person shows up 1st, 2nd, etc. In order to stir things up, we multiply by C(5,4) = C(5,1) to account for all possible positions of the non-voter among the voters.