. An academic department with five faculty members narrowed its choice for department head to either candidate A or candidate B. Each member then voted on a slip of paper for one of the candidates....

. An academic department with five faculty members narrowed its choice for department head to

either candidate A or candidate B. Each member then voted on a slip of paper for one of the

candidates. Suppose there are actually three votes for A and two for B. If the slips are selected for

tallying in random order, what is the probability that A remains ahead of B throughout the vote

count (e.g., this event occurs if the selected ordering is AABAB, but not for ABBAA)?