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A committee has nine members. There are three members that currently serve as the​ board's chairman...

A committee has nine members. There are three members that currently serve as the​ board's chairman comma ranking member comma 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 comma ranking member comma and treasurer. What is the probability of randomly selecting the three members who currently hold the positions of chairman comma ranking member comma and treasurer and reassigning them to their current​ positions?
The probability is _____

math   Statistics-And-Probability   
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Answer: A committee has nine members. There are three members that currently serve as the​ board's chairman comma ranking member comma 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 comma ranking member comma and treasurer. What is the probability of randomly selecting the three members who currently hold the positions of chairman comma ranking member comma and treasurer and reassigning them to their current​ positions?

Solution:

Total members = 9

Selecting 3 members from 9 committee members:

9P3 = 504

number of ways of reassigning the current positions = 1

The probability = 1/504 = 0.001984

Therefore, the probability of randomly selecting the three members who currently hold the positions of chairman, vice chairman, and treasurer and reassigning them to their current​ positions is 0.002.

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