03:48
Probability with Applications in Engineering, Science, and Technology
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 $A A B A B,$ but not for $A B B A A ) ?$