Probability of holding 3 different posts in a committee

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Homework Help Overview

The problem involves selecting three different students from a class of 40 to fill specific roles in a committee: monitor, assistant monitor, and treasurer. The original poster seeks to determine the probability of specific students (A, B, and C) being assigned to these roles.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster calculates the probability for A, B, and C to hold specific roles and questions the probability of them being selected for any of the three posts. Other participants inquire about the reasoning behind the combinatorial calculation used by the original poster.

Discussion Status

Participants are engaging in a dialogue about the calculations and reasoning behind the probabilities. There is an exploration of different arrangements of the selected students and their associated probabilities, indicating a productive direction in understanding the problem.

Contextual Notes

The original poster's calculations suggest a misunderstanding of the total arrangements possible for the roles, which is being discussed among participants. There is also a mention of the need to clarify the reasoning behind the combinatorial approach used.

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Homework Statement


A , B and C are from a class of 40 students. Three students are selected to be a monitor, assistant monitor and treasurer.
a) What's the probability of A to be monitor, B to be assistant monitor , C to be treasurer

my ans is (1/(40 x 39 x 38))=1/59280

b. What's the probability of A , B and C are selected to hold three post?

can someone help me on part b plaese?

my working is 40C3=9880

but the ans is 1/9880


Homework Equations





The Attempt at a Solution

 
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desmond iking said:

Homework Statement


A , B and C are from a class of 40 students. Three students are selected to be a monitor, assistant monitor and treasurer.
a) What's the probability of A to be monitor, B to be assistant monitor , C to be treasurer

my ans is (1/(40 x 39 x 38))=1/59280

b. What's the probability of A , B and C are selected to hold three post?

can someone help me on part b plaese?

my working is 40C3=9880

but the ans is 1/9880


Homework Equations





The Attempt at a Solution


Presumably you wrote down 40C3=9880 for some reason. What is that reason?
 
Ray Vickson said:
Presumably you wrote down 40C3=9880 for some reason. What is that reason?

choose 3 person form 40 person for the 3 posts
 
desmond iking said:
choose 3 person form 40 person for the 3 posts

OK, so now what should you do?

Personally, I would start from the solution to (a) and think about it a bit more: your solution to (a) is for the ordering (monitor,assistant monitor, treasurer) = (A,B,C). However there are other allowed selections, such as (A,C,B) and several others. They all have probabilities of their own, and their total is what you are after.
 

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