Question

a committee has eight members. there are two members that currently serve as the boards chairman and vice chairman. each member is equally likely to serve in any of the positions. two members are randomly selected and assigned to be the new chairman and vice chairman. what is the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and reassigning them to their current positions?

the probability is
(round to four decimal places as needed.)

Explanation:

Step1: Calculate the number of ways to select 2 members out of 8 for the two positions

The number of permutations of \(n\) objects taken \(r\) at a time is given by \(P(n,r)=\frac{n!}{(n - r)!}\). Here \(n = 8\) and \(r=2\), so \(P(8,2)=\frac{8!}{(8 - 2)!}=\frac{8!}{6!}=8\times7 = 56\)

Step2: Calculate the number of favorable outcomes

There is only 1 way to assign the two current members (chairman and vice - chairman) to their current positions.

Step3: Calculate the probability

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P=\frac{1}{56}\approx0.0179\)

Answer:

\(0.0179\)