Probability of Selecting a Committee of 1 from Each Class

[ArcanaNoir]

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?

 

[gb7nash]

How did you get c)? (it's wrong)

 

[tiny-tim]

Hi ArcanaNoir!

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

Your (a) and (b) look ok.

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

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

 

[gb7nash]

(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.

 

[I like Serena]

Funny, I interpreted it as:
only from the group of all juniors and all sophomores.

So: no. sophomores ≥ 0 and no. juniors ≥ 0.

 

[tiny-tim]

Hi I like Serena!

I think that's what it's meant to mean, but I don't think it's what it actually means!

 

[I like Serena]

Hi ^TM!

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

 

[tiny-tim]

uhh?

0 isn't plural ​

 

[tiny-tim]

zero apples isn't apples!

if you have zero apples, you don't have apples ​

 

[I like Serena]

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?

 

[tiny-tim]

no. sophomores ≥ 2 and no. juniors ≥ 2?​

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

Yup!

 

[ArcanaNoir]

Gee guys, if you had just waited.. C was supposed to be only sophomores OR only juniors. My prof's english is bad.

 

[I like Serena]

Wait?!
And miss out on all the fun and conjecture?
Nah!

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!