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How many ways can you group 3 people from 4 sets of twins if no two

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How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post Updated on: 05 Oct 2014, 01:54
3
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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How many ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?

A. 3
B. 16
C. 28
D. 32
E. 56

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Originally posted by Thoughtosphere on 05 Oct 2014, 01:00.
Last edited by Bunuel on 05 Oct 2014, 01:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post 05 Oct 2014, 02:03
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Thoughtosphere wrote:
How many ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?

A. 3
B. 16
C. 28
D. 32
E. 56


As the group shouldn't have siblings in it, then one set of twins can send only one "representative" to the group. The number of ways to choose which 3 sets to send one "representative" to the group is \(C^3_4\) (choosing 3 sets which will be granted the right to send one "representative" to the group);

But each of these 3 sets can send 2 persons to the committee either a brother or a sister: \(2*2*2=2^3\);

So total # of ways is \(C^3_4*2^3=32\).

Answer: D.

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Re: How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post 05 Oct 2014, 01:35
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1
2
Ways to select 3 people from 8 people (4 twins x 2) = 8C3 = 56
Ways to select 1 twin + 1 people = 4C1*6C1 = 24
Ways to select a group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen = 56 - 24 = 32

Ans: D
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Re: How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post 05 Oct 2014, 05:28
1
Thoughtosphere wrote:
How many ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?

A. 3
B. 16
C. 28
D. 32
E. 56


Twins -> a1,a2; b1b2 ; c1c2 ; d1d2


Choose a1 -> b1 -> C1 ; a1->b1->c2 ; a1 ->b2->c1 ; a1 -> b2 -> c2

Therefore 4 ways.

Now The same can be done with a2 as the first choice . So 4*2 = 8 ways

Now instead of abc....we could choose abd or bcd or acd i.e 4 ways [or 4C3 ways]

So 8*4 = 32 ways . Hence Ans D

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How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post 05 Aug 2015, 23:43
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All case number: 8C3=56

Not desired cases: 4C1*6C1=24

56-24=32

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Re: How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post 15 Mar 2019, 07:43
UmangMathur wrote:
How many ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?

A. 3
B. 16
C. 28
D. 32
E. 56


Let the twins be Aa, Bb, Cc, and Dd (where the uppercase letter denotes the older twin and the lowercase letter the younger twin).

We see that we can group: 1) all 3 uppercase letters, 2) all 3 lowercase letters, 3) 2 uppercase and 1 lowercase letters and 4) 1 uppercase and 2 lowercase letters.

Each of the first 2 options has 4C3 = 4 ways, and each of the last 2 options has 4C2 x 4C1 = 6 x 4 = 24 ways. So the total number of ways is( 2 x 4) + (2 x 24) = 8 + 48 = 56.

Answer: E
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Re: How many ways can you group 3 people from 4 sets of twins if no two  [#permalink]

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New post 13 May 2019, 11:10
Top Contributor
UmangMathur wrote:
How many ways can you group 3 people from 4 sets of twins if no two people from the same set of twins can be chosen?

A. 3
B. 16
C. 28
D. 32
E. 56


Take the task of selecting the 3 people and break it into stages.

Stage 1: Select the 3 sets of twins from which we will select 1 sibling each.
There are 4 sets of twins, and we must select 3 of them. Since the order in which we select the 3 pairs does not matter, this stage can be accomplished in 4C3 ways (4 ways)

Stage 2: Take one of the 3 selected sets of twins and choose 1 person to be in the group.
There are 2 siblings to choose from, so this stage can be accomplished in 2 ways.

Stage 3: Take one of the 3 selected sets of twins and choose 1 person to be in the group.
There are 2 siblings to choose from, so this stage can be accomplished in 2 ways.

Stage 4: Take one of the 3 selected sets of twins and choose 1 person to be in the group.
There are 2 siblings to choose from, so this stage can be accomplished in 2 ways.

By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus create a 3-person committee) in (4)(2)(2)(2) ways (= 32 ways)

Answer: D

Cheers,
Brent

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: How many ways can you group 3 people from 4 sets of twins if no two   [#permalink] 13 May 2019, 11:10
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