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 totally in random order, what is the probability that A remains ahead of B through out the vote count ( e.g. , this event occurs if the selected ordering is AABAB, but not for ABBAA)?

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Asked Sep 8, 2019

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 totally in random order, what is the probability that A remains ahead of B through out the vote count ( e.g. , this event occurs if the selected ordering is AABAB, but not for ABBAA)?

check_circleExpert Solution
Step 1

Number of ways to select the votes for B:

There are 2 votes for B out of 5 votes. Thus, there a...

5!
5C2
2!(5 2)
5x 4x 3!
(2x 1)3!
= 10
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5! 5C2 2!(5 2) 5x 4x 3! (2x 1)3! = 10

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