Question

A committee has

sevenseven

members. There are

threethree

members that currently serve as the​ board's

chairman commachairman,

vice chairman commavice chairman,

andand

treasurertreasurer.

Each member is equally likely to serve in any of the positions.

ThreeThree

members are randomly selected and assigned to be the new

chairman commachairman,

vice chairman commavice chairman,

andand

treasurertreasurer.

What is the probability of randomly selecting the

threethree

members who currently hold the positions of

chairman commachairman,

vice chairman commavice chairman,

andand

treasurertreasurer

and reassigning them to their current​ positions?

The probability is

 

nothing.

Answer 1

There is only one way of selecting this group from seven members ie out of 7C₃ ways Therefore the Probability of selecting this particular group of three persons from the 7 member comitee is 1/ 7C₃. If the same set of people is selected, They can be randomly arranged in three different positions in 3! ways= 3*2*1=6 diffferent ways. Hence the probability of getting the same arrangement is 1/6. Let A be the event of getting the same arrangement or reaasiigning to their current position and B be the event of selecting the same group.