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

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Manager
Joined: 18 Aug 2010
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In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 06:33
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55% (hard)

Question Stats:

38% (01:14) correct 63% (01:08) wrong based on 40 sessions

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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 one freshman and one sophomore?

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

[Reveal] Spoiler:
im not getting # of possible 2-person groups PlZ help , thx

[Reveal] Spoiler: OA

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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 07:04
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Total number of ways to select 2 students from any two groups =

$$C^4_2*C^2_1*C^2_1 = 4*(3/2)*2*2 = 24$$

$$C^4_2$$ -- Number of ways to select 2 groups out of 4 groups
$$C^2_1$$ -- Number of ways to select 1 student from 1 of the selected groups
$$C^2_1$$ -- Number of ways to select 1 student from 2nd selected group

There are total 24 ways in which you can select two students from any two groups.

Selecting 2 students, one each from freshmen and sophomore = $$C^2_1*C^2_1=2*2=4$$

P = 4/24 = 1/6.
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 07:10
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Number of ways in which you can form a group of two where both are from same class is 4C1 = 4

Total number of ways in which a group of two can be formed is 8C2 = 28

Number of ways in which the group of two can be formed such that both are not from the same class are = 28 - 4 = 24 ways

Number of ways of forming a group when one is a Sophomore and 1 is a Freshman is:

2C1 x 2C1 (One Sophomore AND One Freshman)

= 2 x 2 = 4

Probability = 4/24 = 1/6
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Kudos [?]: 238 [1], given: 78

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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 07:14

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Manager
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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17 Mar 2011, 10:33
thx guys
+ kudos from me

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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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06 Aug 2017, 12:21
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, [#permalink]

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18 Aug 2017, 03:06
f =2 , s=2 , j=2 and sn=2
total =8 students
2 are to be selected from 8 such that each is different.

total no. of ways to select 2 from 8= 8C2= 28
number of ways 2 are same = 4 (f,s,j,sn )
28-4=24

selecting 1 freshman from 2, and 1 sophomore from 2 = (2C1 x 2C1)/24= 4/24
=1/6 ANS

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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,   [#permalink] 18 Aug 2017, 03:06
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