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

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

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17 Mar 2011, 05:33
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Difficulty:

95% (hard)

Question Stats:

29% (02:06) correct 71% (02:01) wrong based on 146 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 2-person groups PlZ help , thx

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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, 06:04
6
1
3
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, 06:10
2
1
1
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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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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In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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15 Dec 2018, 19:14
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Can someone tell me why can't we select the two students from 2 different grades like this= 8C1 * 6C1 ?
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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16 Dec 2018, 15:26
1
2c1*2c1/4c2*2c1*2c1
=> 1/4c2

=> 1/6

Posted from my mobile device
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In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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20 Dec 2018, 09:22
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Probability of choosing a freshman : 1/4

Probability of choosing a sophomore after that : 2/6 = 1/3

Combined probability : 1/4 * 1/3 = 1/12. Also consider the case where a sophomore is chosen first. For that multiply the result with 2.

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

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03 Jan 2019, 19:09
can someone explain to me why not C? is it because the rules is the students have to come from different grades?
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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31 Jan 2019, 16:45
Condition:
Cant select 2 students from same group.

2FRSH(AB), 2SOPH(CD) , 2JUNI(EF) , 2SNR (GH)

Ways to select 1 FRSH and SOPH
AC---CA
BC---CB
BD---DB
Thus 2 students can be selected in 8 ways only from FRSH and SOPH

Prob= 1/8*1/6=1/48 (since we cannot choose another student from the same grp)
Now 8 ways to choose =8/48 =1/6
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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31 Jan 2019, 21:40
1
mohit2051 wrote:
Can someone tell me why can't we select the two students from 2 different grades like this= 8C1 * 6C1 ?

Hi Mohit,

You have to divide $$8c1$$ * $$6c1$$ by 2 to get the correct answer

For ex : let us say 1 Junior and 1 Senior have been finally selected

Junior could be selected first (out of 8 ) and then Senior could be selected (out of 6)

or

Senior could be selected first (out of 8 ) and then Junior could be selected (out of 6)

You can see that the same combination is being counted twice

So the correct answer for total number of ways is $$\frac{8c1 * 6c1}{2}$$ = 24

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

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05 Feb 2019, 16:29
tinki wrote:
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

Great question. I definitely got tricked.

I calculated the total combinations possible by doing 8c2 and got 28 but did not subtract out the combinations where the 2 representatives are from the same group. TRICKY!
Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,   [#permalink] 05 Feb 2019, 16:29