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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, 06:33
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Question Stats:

28% (02:02) correct 72% (02:01) wrong based on 142 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


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, 07:04
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1
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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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New post 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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New post 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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In a high school debating team consisting of 2 freshmen, 2 sophomores,  [#permalink]

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New post 15 Dec 2018, 20:14
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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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New post 16 Dec 2018, 16:26
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2c1*2c1/4c2*2c1*2c1
=> 1/4c2

=> 1/6

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

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New post 20 Dec 2018, 10:22
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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.

Answer = 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 03 Jan 2019, 20:09
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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New post 31 Jan 2019, 17:45
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
AD---DA
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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New post 31 Jan 2019, 22:40
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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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New post 05 Feb 2019, 17:29
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!
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Re: In a high school debating team consisting of 2 freshmen, 2 sophomores,   [#permalink] 05 Feb 2019, 17:29
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