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# A group of seven research scholars needs to be divided into three team

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Manager
Joined: 07 Jun 2017
Posts: 174
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38
GPA: 3.6
WE: Information Technology (Computer Software)
A group of seven research scholars needs to be divided into three team  [#permalink]

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01 Nov 2017, 22:39
00:00

Difficulty:

45% (medium)

Question Stats:

63% (01:38) correct 37% (02:13) wrong based on 76 sessions

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A group of seven research scholars needs to be divided into three teams comprising of 2, 3, and 2 members respectively. How many different teams are possible?

A. 840
B. 420
C. 210
D. 140
E. 70

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Naveen
email: nkmungila@gmail.com
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Intern
Joined: 26 Aug 2017
Posts: 2
Re: A group of seven research scholars needs to be divided into three team  [#permalink]

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02 Nov 2017, 01:57
nkmungila wrote:
A group of seven research scholars needs to be divided into three teams comprising of 2, 3, and 2 members respectively. How many different teams are possible?

A. 840
B. 420
C. 210
D. 140
E. 70

So lets select 2 member team from total of 7 = 7C2 = 21
Now we select 3 member team from remaining 5 = 5C3 = 10
Now we are left to select 2 from left 2 = 2C2 = 1

Now possibility of selecting them all = 7C2*5C3*2C2 = 210

Hence C

Now if u want to select 3 team first then the 2's then also the answer remain same, i.e. 7C3*4C2*2C2 = (35)(6)(1) = 210
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Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India
A group of seven research scholars needs to be divided into three team  [#permalink]

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02 Nov 2017, 02:15
nkmungila wrote:
A group of seven research scholars needs to be divided into three teams comprising of 2, 3, and 2 members respectively. How many different teams are possible?

A. 840
B. 420
C. 210
D. 140
E. 70

The question doesn't say that the teams are distinct by name. I would say that there is ambiguity here. I don't understand the use of the word "respectively" here.

So solution according to me would be:

Let's select the group of 3 first: 7C3 = 35

Next, we select 2 for the first group of 2 in 4C2 ways. The leftover 2 for the second group of 2 will be picked in 2C2 ways. This gives us 4C2*2C2 = 6 ways of picking them.
But note that the two groups of 2 each are not distinct so we need to divide them by 2! to un-arrange.

This means total number of teams possible = 35*6/2 = 105

What is the source of this problem?
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Joined: 02 Jul 2017
Posts: 1
Re: A group of seven research scholars needs to be divided into three team  [#permalink]

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04 Nov 2017, 03:13
hi dear,

what mean of 7C2 = 21 . C?

thank and appreciate for explanation.
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Joined: 02 Sep 2009
Posts: 50007
Re: A group of seven research scholars needs to be divided into three team  [#permalink]

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04 Nov 2017, 03:17
Re: A group of seven research scholars needs to be divided into three team &nbs [#permalink] 04 Nov 2017, 03:17
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