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Eight persons in an organization including A and B

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Intern
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Eight persons in an organization including A and B  [#permalink]

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New post 16 Jan 2016, 23:41
7
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (02:23) correct 36% (02:18) wrong based on 90 sessions

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Eight persons in an organization including A and B were to be divided in two groups of 4 members each. The total number of groups containing both A and B is what fraction of the total number of groups which can be formed?

1/4
1/70
3/14
1/10
11/14
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V
Joined: 02 Aug 2009
Posts: 7578
Re: Eight persons in an organization including A and B  [#permalink]

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New post 17 Jan 2016, 00:10
1
jyotibrata wrote:
Eight persons in an organization including A and B were to be divided in two groups of 4 members each. The total number of groups containing both A and B is what fraction of the total number of groups which can be formed?

1/4
1/70
3/14
1/10
11/14


The fraction is nothing but the probability..

Number to choose 4 out of 8= 8C4..
Number to choose A and B and 2 from remaining 6=6C2..
prob of A and B choosen=6C2/8C4= {6!/4!2!}/{8!/4!4!}..
6!4!4!/8!4!2!=3/2*7=3/14
C
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Re: Eight persons in an organization including A and B  [#permalink]

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New post 20 Apr 2016, 04:55
This question is not a DS question so why is it tagged as 'DS'
Manager
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Re: Eight persons in an organization including A and B  [#permalink]

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New post 20 Apr 2016, 17:10
The 8 people need to be divided in 2 (similar) groups of 4 each. So the ordering of the groups will not matter here.
This can be achieved in 8C4 ways= 8! / (4! * 4!)

The number of groups that contain both A and B will be 6C4 (4 in one group , and 2 in the group with A and B)= 6!/ (4! * 2!)

The Fraction asked = 6!/ (4! * 2!) / 8! / (4! * 4!)
= 3/14

Correct Option : C
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Re: Eight persons in an organization including A and B  [#permalink]

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New post 22 Jul 2017, 13:36
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Re: Eight persons in an organization including A and B   [#permalink] 22 Jul 2017, 13:36
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