Twenty faculty members in a certain department have just participated in a department chair election. Suppose that candidate A has received 12 of the votes and candidate B the other 8 votes. If the ballots are opened one by one in random order and the candidate selected on each ballot is recorded, use simulation to estimate the probability that candidate A remains ahead of candidate B throughout the vote count (which happens if, for example, the result is AA…AB…B but not if the result is AABABB…).