A committee has thirteen thirteen members. There are three three members that cu

Question

A committee has thirteen thirteen members. There are three three members that currently serve as the board's chairman comma chairman, vice chairman comma vice chairman, and and treasurer treasurer. Each member is equally likely to serve in any of the positions. Three Three members are randomly selected and assigned to be the new chairman comma chairman, vice chairman comma vice chairman, and and treasurer treasurer. What is the probability of randomly selecting the three three members who currently hold the positions of chairman comma chairman, vice chairman comma vice chairman, and and treasurer treasurer and reassigning them to their current positions?

Explanation / Answer

There are 13 members. Each member is equally likely to get any position.

Ways in which we can select 3 people out of 13 are 13C3 , these 3 members can themselves arrange among each other, so 3! ways to arrange them.

Total ways to select 3 people is 13C3 x 3!

Out of all these ways there's only one way from which we can select old combination of members, So the probability of selecting same members again is

1/(13C3 x 3! )

=> 1/1716

=> 0.00058275058

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