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Math Expert V
Joined: 02 Sep 2009
Posts: 59125
From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (01:54) correct 37% (01:48) wrong based on 120 sessions

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From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) $$\frac{1}{10}$$

(B) $$\frac{1}{6}$$

(C) $$\frac{1}{5}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{3}$$

Project PS Butler

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Senior Manager  G
Joined: 29 Jun 2019
Posts: 467
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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1
2
The total ways to select 4 people from 6 people are,6C4=15
the ways that number of juniors are more than sophomores are made by 3C3 *3C1=1*3=3
Hence,3/15=1/5
Option C

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GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5283
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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total students; 6
for 4 we have possiblity ; 6c4 ; 15
so for J>H ;
3c3*3c1 ;3
3/15 ; 1/5

IMO C

Bunuel wrote:
From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) $$\frac{1}{10}$$

(B) $$\frac{1}{6}$$

(C) $$\frac{1}{5}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{3}$$

Project PS Butler

Intern  B
Joined: 28 Mar 2019
Posts: 7
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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Archit3110 wrote:
total students; 6
for 4 we have possiblity ; 6c4 ; 15
so for J>H ;
3c3*3c1 ;3
3/15 ; 1/5

IMO C

Bunuel wrote:
From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) $$\frac{1}{10}$$

(B) $$\frac{1}{6}$$

(C) $$\frac{1}{5}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{3}$$

Project PS Butler

Hi Archit3110, can you clarify the reasoning beyond the statement that the total possibilities for J's to be more than S's is 3C3*3C1 = 3 ?

I can think of only three possible arrangements ( J J J S - J J S S - J S S S) so why is the probability 3? Is it because we have three different possible people who can occupy the "S" position in arrangement J J J S ?
Thank you very much
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5283
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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CeciliaB wrote:
Archit3110 wrote:
total students; 6
for 4 we have possiblity ; 6c4 ; 15
so for J>H ;
3c3*3c1 ;3
3/15 ; 1/5

IMO C

Bunuel wrote:
From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) $$\frac{1}{10}$$

(B) $$\frac{1}{6}$$

(C) $$\frac{1}{5}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{3}$$

Project PS Butler

Hi Archit3110, can you clarify the reasoning beyond the statement that the total possibilities for J's to be more than S's is 3C3*3C1 = 3 ?

I can think of only three possible arrangements ( J J J S - J J S S - J S S S) so why is the probability 3? Is it because we have three different possible people who can occupy the "S" position in arrangement J J J S ?
Thank you very much

hello CeciliaB

for this question there would be only 1 way of selecting J>S i.e JJJS which can be written in combination terms as 3c3 *3c1 ; 3*1; 3
total head count is 6 ; 3 J +3S ; and we need to choose 4 out of 6 so total fair chances ; 6c4 ; 15
Hence the Probability of having J>S where total draw is for 4 would be 3/15 ; 1/5

Hope this helps
SVP  P
Joined: 03 Jun 2019
Posts: 1849
Location: India
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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Bunuel wrote:
From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) $$\frac{1}{10}$$

(B) $$\frac{1}{6}$$

(C) $$\frac{1}{5}$$

(D) $$\frac{1}{4}$$

(E) $$\frac{1}{3}$$

Project PS Butler

Total number of ways = 6C4 = 15
Number of favourable ways = 3C3*3C1 = 3

Probability = 3/15 = 1/5

IMO C
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Director  P
Joined: 24 Nov 2016
Posts: 783
Location: United States
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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Bunuel wrote:
From a group of 3 sophomores and 3 juniors, 4 students are to be randomly selected. What is the probability that more juniors than sophomores will be selected?

(A) $$\frac{1}{10}$$
(B) $$\frac{1}{6}$$
(C) $$\frac{1}{5}$$
(D) $$\frac{1}{4}$$
(E) $$\frac{1}{3}$$

probability: favorable outcomes / total outcomes
favorable: JJJS…3C3•3C1=1•3=3
total: 6C4=15
prob: 3/15=1/5

Intern  B
Joined: 13 Jan 2019
Posts: 4
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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This is a similar question. I have a doubt as to why 0 boys are taken in this but In the above question 1 Sophomore Is taken mandatory

q
From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected?

A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

Posted from my mobile device Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando   [#permalink] 02 Nov 2019, 02:48
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