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

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Senior Manager
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Joined: 22 Feb 2018
Posts: 324
From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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New post 27 Aug 2018, 12:21
1
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

67% (01:11) correct 33% (01:51) wrong based on 18 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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Senior Manager
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Joined: 07 Oct 2017
Posts: 273
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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New post 27 Aug 2018, 13:12
Princ 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) \(\frac{1}{3}\)
3c3 ways of choosing juniors and 4c1 at of choosing sophomores is the only way juniors > sophomores

Total ways = 6c4

Answer is C


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Joined: 02 Sep 2015
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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 27 Aug 2018, 14:19
P(Total) = 6C4 = 15
P(Selecting max juniors) = P(Selecting 3 Juniors (All) and 1 Sophomore) = 3C3 * 3C1 = 1 * 3 = 3

=> P(Selecting max juniors) / P(Total)
=> 3/15
=> 1/5
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando &nbs [#permalink] 27 Aug 2018, 14:19
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