What is the Correct Probability of a Student Becoming Chairperson?

[Shawn Garsed]

Homework Statement

A. Mrs. Moyer’s class has to choose 4 out of 12 people to serve on an activity
committee.
B. The four chosen students are then selected for the positions of chairperson, activities
planner, activity leader, and treasurer.

What is the probability that anyone of the students is chosen to be the
chairperson?

Homework Equations

Permutations and combinations

The Attempt at a Solution

I first calculated the number of outcomes for part A: 12!/((12-4)!4!)=495. Then I calculated the number of outcomes for part B: 4!=24. Which gives the total number of outcomes: 495*24=11880.

After that, I calculated the favorable number of outcomes for A and B:

A: (1*11*10*9)/3!=165

B: 1*3*2*1=6

Which gives the total number of outcomes: 165*6=990.

Therefore, the probality is 990/11880 or 1/12.
The problem is that the book says it's 1/2970.

Who's right?

Thanks in advance,

Shawn

 

[sebb1e]

Are you quite sure that's the question being asked?

As you've phrased the question, it has to be 1/12 because part A is irrelevant, all students have equal chance of being the chairperson.

 

[Shawn Garsed]

That's exactly how the question is phrased. I even calculated it in different ways, the simplest being: 4 out of 12 means you have a 4/12 or 1/3 chance of being chosen and the chance of being chosen as chairperson is 1/4. (1/3)*(1/4)=1/12.

 

[sebb1e]

Well you are right about there being 1180 different combinations of 4 students. 2970 is a quarter of 1180 so it's not a totally random number but it definitely isn't the answer to your question.