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

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

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New post 01 Nov 2017, 22:39
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A
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C
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E

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Question Stats:

73% (01:07) correct 27% (01:58) wrong based on 52 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
[Reveal] Spoiler: OA

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Re: A group of seven research scholars needs to be divided into three team [#permalink]

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New post 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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A group of seven research scholars needs to be divided into three team [#permalink]

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New post 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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Re: A group of seven research scholars needs to be divided into three team [#permalink]

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New post 04 Nov 2017, 03:13
hi dear,

what mean of 7C2 = 21 . C?

thank and appreciate for explanation.

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Re: A group of seven research scholars needs to be divided into three team [#permalink]

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New post 04 Nov 2017, 03:17
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hew wrote:
hi dear,

what mean of 7C2 = 21 . C?

thank and appreciate for explanation.


C stands for combinations: \(7C2=\frac{7!}{2!(7-2)!}=21\).

21. Combinatorics/Counting Methods



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