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# In a high school debating team consisting of 2 freshmen, 2

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Director
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In a high school debating team consisting of 2 freshmen, 2 [#permalink]  24 Dec 2004, 05:23
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In a high school debating team consisting of 2 freshmen, 2 sophomores, 2 juniors, and 2 seniors, two students are selected to represent the school at the state debating championship. The rules stipulate that the representatives must be from different grades, but otherwise the 2 representatives are to be chosen by lottery. What is the probability that the students selected will consist of one freshman and one sophomore?

A. 1/16
B. 1/8
C. 1/7
D. 1/6
E. 1/4

HIGHTLIGHT BELOW TO SEE OA:
OA is (D)

I tried to solve this a different way but encounter a different result. Please look
P(p(1st freshman AND 2nd sophomore) OR p(1st sophomore AND 2nd freshman)
=p1 + p2
=(2/8 * 2/7) + (2/8 * 2/7) (7 because one person already choosen, so OUT)
=1/14 + 1/14
=1/7
This is different from OA. Anyone can point out the problem with solution above?
Manager
Joined: 13 Dec 2004
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[#permalink]  24 Dec 2004, 13:23
Quote:
tried to solve this a different way but encounter a different result. Please look

P(p(1st freshman AND 2nd sophomore) OR p(1st sophomore AND 2nd freshman)
=p1 + p2
=(2/8 * 2/7) + (2/8 * 2/7) (7 because one person already choosen, so OUT)
=1/14 + 1/14
=1/7
This is different from OA. Anyone can point out the problem with solution above?

I'll give it a try.
I think what you want is P(F1 & So1) + P(F1 & So2) + P(F2 + So1) + P(F2 + So2). There are four possible desireable outcomes. Since there are 24 possible outcomes, I get 4/24, which is 1/6.

Doing it your way, I think you would want to do it like this:
[P(choosing a freshman first) + P(choosing a sophomore second)] + [P(choosing a sophomore first) + P(choosing a freshman second)] =

(1/4 x 2/6) + (1/4 + 2/6) = 4/24 = 1/6

Your denominator was 7, when it should have been 6, because there was a requirement that the two students be from different grades, so once a student is chosen, the other student in his/her grade can't be chosen.
Senior Manager
Joined: 19 Sep 2004
Posts: 371
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[#permalink]  25 Dec 2004, 13:05
Hi I am kind of lost!

My way was:

(2C1*2C1)
------------= 2*2
8C2 ----- = 1/7
8*7/2

The order dosen't matter rt?I am kind of lost.
Please help. Hil..I was not able to understand your apporach.I gues syou have some "+" "*" prob in your post. Please check

Thanks
Saurabh Malpani
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[#permalink]  25 Dec 2004, 19:44
hilairity wrote:
Quote:
tried to solve this a different way but encounter a different result. Please look

P(p(1st freshman AND 2nd sophomore) OR p(1st sophomore AND 2nd freshman)
=p1 + p2
=(2/8 * 2/7) + (2/8 * 2/7) (7 because one person already choosen, so OUT)
=1/14 + 1/14
=1/7
This is different from OA. Anyone can point out the problem with solution above?

I'll give it a try.
I think what you want is P(F1 & So1) + P(F1 & So2) + P(F2 + So1) + P(F2 + So2). There are four possible desireable outcomes. Since there are 24 possible outcomes, I get 4/24, which is 1/6.

Doing it your way, I think you would want to do it like this:
[P(choosing a freshman first) + P(choosing a sophomore second)] + [P(choosing a sophomore first) + P(choosing a freshman second)] =

(1/4 x 2/6) + (1/4 + 2/6) = 4/24 = 1/6

Your denominator was 7, when it should have been 6, because there was a requirement that the two students be from different grades, so once a student is chosen, the other student in his/her grade can't be chosen.

24 possible outcomes? didn't get that..
Intern
Joined: 17 Dec 2004
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[#permalink]  26 Dec 2004, 02:38
There should be 28 total possible outcome, calculated by 8C2 (or by counting 7+6+5+4+3+2+1=28). However, as the question says "the representative should be from different grade.......so 28 - 4 = 24.

Total outcome for one F + one SO is 4 (i.e. F1+SO1, F1+SO2, F2+SO1 and F2+SO2) - Order is not important....

So....it should be 4/24 = 1/6
Manager
Joined: 29 Jul 2004
Posts: 63
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[#permalink]  27 Dec 2004, 11:06
Hcgmat wrote:
There should be 28 total possible outcome, calculated by 8C2 (or by counting 7+6+5+4+3+2+1=28). However, as the question says "the representative should be from different grade.......so 28 - 4 = 24.

Total outcome for one F + one SO is 4 (i.e. F1+SO1, F1+SO2, F2+SO1 and F2+SO2) - Order is not important....

So....it should be 4/24 = 1/6

How did you figure out to subtract 4 from the 28. I got 4/28, but didn't know how to eliminate the ways where the representatives were in the same grade.
[#permalink] 27 Dec 2004, 11:06
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# In a high school debating team consisting of 2 freshmen, 2

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