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) ? ?

Answer: Step 1: Given, 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. Here we have to find 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)