Question

a committee has fourteen members. there are three members that currently serve as the boards chairman, ranking member, and treasurer. each member is equally likely to serve in any of the positions. three members are randomly selected and assigned to be the new chairman, ranking member, and treasurer. what is the probability of randomly selecting the three members who currently hold the positions of chairman, ranking member, and treasurer and reassigning them to their current positions?
the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate the number of permutations of selecting 3 members out of 14

The formula for permutations \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 14\) and \(r=3\).

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Step2: Calculate the number of favorable outcomes

There is only 1 way to re - assign the three members to their current positions.

Step3: Calculate the probability

The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{1}{2184}\approx0.0005\)

Answer:

\(0.0005\)