Probability of Selecting a Committee of 1 from Each Class

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Homework Help Overview

The problem involves selecting a committee of size 4 from a group of students divided into classes: freshmen, sophomores, juniors, and seniors. The original poster presents multiple scenarios for the composition of the committee, including specific class distributions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the calculations for the probability of selecting committees with specific class distributions, questioning the correctness of the original poster's attempts.
  • There is confusion regarding the interpretation of the third scenario, with participants exploring different meanings of "only sophomores and juniors."
  • Some participants suggest that the wording may imply different conditions for the committee composition.

Discussion Status

The discussion is active, with participants providing feedback on the original poster's calculations and interpretations. There is no explicit consensus on the meaning of the third scenario, and various interpretations are being explored.

Contextual Notes

Participants note potential ambiguities in the problem statement, particularly regarding the phrasing of the third scenario, which may lead to different interpretations of the committee composition requirements.

ArcanaNoir
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Homework Statement



From a group of 3 freshman, 4 sophomores, 4 juniors, and 3 seniors, a committee of size 4 is randomly selected. Find the probability that the committee will consist of:

a) 1 from each class
b) 2 sophomores and 2 juniors
c) only sophomores and juniors

Homework Equations



How do you write "x choose n" in latex? For now I'll write (xCn)


The Attempt at a Solution



I figured there (14C4) different committees, giving 1001 committees.

a) [(3C1)(4C1)(4C1)(3C1)]/1001 = 144/1001

b) [(4C2)(4C2)]/1001 = 36/1001

c) 2/1001


Is this correct?
 
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How did you get c)? (it's wrong)
 
Hi ArcanaNoir! :smile:

(try using the X2 and X2 icons just above the Reply box … alternative nCm in latex is ^nC_m :wink:)

Your (a) and (b) look ok. :smile:

Your (c) is the answer for "only sophomores or only juniors". :redface:

(frankly, I don't know what (c) means … eg is 1 sophomore and 3 juniors sophomores ?)
 
tiny-tim said:
(frankly, I don't know what (c) means … eg is 1 sophomore and 3 juniors sophomores ?)

I agree. c) is poorly worded. I think the only condition is that no. sophomore >= 1 and no. junior >= 1, otherwise it's the same question as b), or 2 like the OP said.
 
Funny, I interpreted it as:
only from the group of all juniors and all sophomores.

So: no. sophomores ≥ 0 and no. juniors ≥ 0.
 
Last edited:
Hi I like Serena! :smile:

I think that's what it's meant to mean, but I don't think it's what it actually means! :biggrin:
 
Hi TM! :smile:

Errr... so 0 juniors and 4 sophomores, would qualify,
but 1 junior and 3 sophomores would not? :confused:
 
uhh? :confused:

0 isn't plural :wink:
 
zero apples isn't apples!

if you have zero apples, you don't have apples :redface:
 
  • #10
Okay.

So are you suggesting that c) could be interpreted as:
no. sophomores ≥ 2 and no. juniors ≥ 2?​
Or more strongly, that this is what it actually means?
 
Last edited:
  • #11
I like Serena said:
no. sophomores ≥ 2 and no. juniors ≥ 2?​


Or more strongly, that this is what it actually means?

Yup! :biggrin:
 
  • #12
Gee guys, if you had just waited.. C was supposed to be only sophomores OR only juniors. My prof's english is bad.
 
  • #13
Wait?!
And miss out on all the fun and conjecture?
Nah! :smile:

Anyway, I was kind of impressed to find out that "only sophomores and juniors" translates into "exactly 2 sophomores and 2 juniors".
Who'd have thunk! :wink:
 

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