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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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Question Stats:
40% (01:33) correct 60% (01:09) wrong based on 62 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 im not getting # of possible 2person 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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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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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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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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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 ) 284=24
selecting 1 freshman from 2, and 1 sophomore from 2 = (2C1 x 2C1)/24= 4/24 =1/6 ANS




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