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# The only contents of a container are 4 blue disks and 8 gree

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Senior Manager
Joined: 06 Aug 2011
Posts: 341
The only contents of a container are 4 blue disks and 8 gree  [#permalink]

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07 Jan 2014, 04:43
2
10
00:00

Difficulty:

15% (low)

Question Stats:

85% (02:32) correct 15% (02:44) wrong based on 170 sessions

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The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?

A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220

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Joined: 02 Sep 2009
Posts: 50016
The only contents of a container are 4 blue disks and 8 gree  [#permalink]

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07 Jan 2014, 04:51
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3
sanjoo wrote:
The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?

A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220

APPROACH #1:

$$P(BGG) = \frac{C^1_4*C^2_8}{C^3_{12}}=\frac{4*28}{220}=\frac{28}{55}$$.

APPROACH #2:

$$P(BGG) =\frac{3!}{2!}*\frac{4}{12}*\frac{8}{11}*\frac{7}{10}=\frac{28}{55}$$. We need to multiply by 3!/2! because BGG scenario can occur in several ways: BGG, GBG, GGB (permutations of 3 letters BGG).

Hope it's clear.
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GMAT Date: 02-04-2014
Re: The only contents of a container are 4 blue disks and 8 gree  [#permalink]

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07 Jan 2014, 10:30
1
sanjoo wrote:
The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?

A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220

Prob of selecting one blue and two green is (4*8*7/12*11*10)
one blue and two green can be arranged in 3!/2! ways
hence the prob becomes 3*4*8*7/12*11*10=28/55
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Joined: 06 Nov 2014
Posts: 1883
Re: The only contents of a container are 4 blue disks and 8 gree  [#permalink]

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28 Feb 2015, 07:09
1
sanjoo wrote:
The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?

A. 21/55
B. 28/55
C. 34/55
D. 5/8
E. 139/220

1st Blue disk can be selected in 4C1 = 4 ways
1st Green disk can be selected in 8C1 = 8 ways
2nd Green disk (without replacement) can be selected in 7C1 = 7 ways

1 blue disk can be selected out of total 12 disks in 12C1 = 12 ways
1 green disk can be selected out of remaining 11 disks in 11C1 = 11 ways
2nd green disk can be selected out of remaining 10 disks in 10C1 = 10 ways
Probability = (4*8*7)/(12*11*10)

But, the order of ONE blue and TWO green could be arranged in 3!/2! ways.
So total probability = 3!/2! * (4*8*7)/(12*11*10)
= 28/55
Hence option B.

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Re: The only contents of a container are 4 blue disks and 8 gree  [#permalink]

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29 Jun 2017, 22:32
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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The only contents of a container are 4 blue disks and 8 gree &nbs [#permalink] 29 Jun 2017, 22:32
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