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

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

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New post 17 Mar 2011, 05:33
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Question Stats:

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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

im not getting # of possible 2-person groups :( PlZ help , thx


Answer: Probability: 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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New post 17 Mar 2011, 06:04
4
1
2
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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New post 17 Mar 2011, 06:10
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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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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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

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New post 17 Mar 2011, 09:33
thx guys :)
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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New post 18 Aug 2017, 02:06
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]

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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores, &nbs [#permalink] 23 Aug 2018, 10:43
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