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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
Joined: 22 Feb 2018
Posts: 416
From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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27 Aug 2018, 11:21
1
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:12) correct 27% (01:51) wrong based on 22 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
Joined: 07 Oct 2017
Posts: 260
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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27 Aug 2018, 12:12
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

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Intern
Joined: 02 Sep 2015
Posts: 42
Re: From a group of 3 sophomores and 3 juniors, 4 students are to be rando  [#permalink]

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27 Aug 2018, 13:19
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, 13:19
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