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# From a group of 3 sophomores and 3 juniors, 4 students are to be rando

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Math Expert
Joined: 02 Sep 2009
Posts: 64891
From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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29 Aug 2019, 21:54
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Difficulty:

55% (hard)

Question Stats:

59% (01:53) correct 41% (02:00) wrong based on 192 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) $$\frac{1}{3}$$

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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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29 Aug 2019, 22:03
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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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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30 Aug 2019, 09:42
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
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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31 Aug 2019, 17:52
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
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Posts: 6412
Location: India
Concentration: Sustainability, Marketing
GPA: 4
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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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01 Sep 2019, 00:31
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
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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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02 Oct 2019, 10:36
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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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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14 Oct 2019, 05:58
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
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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02 Nov 2019, 01:48
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

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Joined: 13 May 2020
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From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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13 May 2020, 09:29
Hi, I'm still having a difficult time wrapping my head around how many combinations of 3 juniors and 1 sophomore can be made. While I understand conceptually that you must multiply (3)(1) = 3, however when I actually write out all of the possible combinations, I get (1) SJJJ, (2) JSJJ, (3) JJSJ, and (4) JJJS - for a total of 4 combinations, not 3.

How do I reconcile this disconnect?
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Joined: 02 Sep 2009
Posts: 64891
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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13 May 2020, 09:45
stephele99 wrote:
Hi, I'm still having a difficult time wrapping my head around how many combinations of 3 juniors and 1 sophomore can be made. While I understand conceptually that you must multiply (3)(1) = 3, however when I actually write out all of the possible combinations, I get (1) SJJJ, (2) JSJJ, (3) JJSJ, and (4) JJJS - for a total of 4 combinations, not 3.

How do I reconcile this disconnect?

You are arranging 4 units out of which 3 are identical: SJJJ.

That's not what 3C3*3C1 = 3 represents. There are 3 ways to choose 3 juniors (out of 3) and 1 sophomore (out of 3). Say there are 3 juniors (A, B, C) and 3 sophomores (x, y, z). We can have:

(A, B, C - x)
(A, B, C - y)
(A, B, C - z)
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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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16 May 2020, 08:26
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) $$\frac{1}{3}$$

If the four people consist of more juniors than seniors, then there must be 3 juniors and 1 senior.

The probability of selecting 3 juniors and 1 senior is:

(3C3 * 3C1) / 6C4 = (1 x 3) / [(6 x 5 x 4 x 3) / (4 x 3 x 2)] = 3/15 = 1/5.

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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando   [#permalink] 16 May 2020, 08:26