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

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

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New post 29 Aug 2019, 22:54
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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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New post 29 Aug 2019, 23:03
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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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New post 30 Aug 2019, 10:42
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) \(\frac{1}{3}\)

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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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New post 31 Aug 2019, 18:52
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) \(\frac{1}{3}\)

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

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New post 01 Sep 2019, 01:31
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


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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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New post 02 Oct 2019, 11:36
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) \(\frac{1}{3}\)

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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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New post 14 Oct 2019, 06:58
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

Answer (C)
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Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando   [#permalink] 14 Oct 2019, 06:58
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