A committee of 3 people is to be chosen from four married : GMAT Problem Solving (PS) - Page 2
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 02:12

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A committee of 3 people is to be chosen from four married

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7068

Kudos [?]: 92951 [0], given: 10541

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

07 Nov 2012, 04:37
Expert's post
1
This post was
BOOKMARKED
watwazdaquestion wrote:
is this a correct way to get the answer? or was it just coincidence:

8C3 - 4(4C2) = 56 - 4(6) = 32

It's not clear what is the logic behind the formula.

Reversed approach would be:
There are 8C3=56 ways to select 3 people out of 8 without any restriction;
There are 4C1*6=24 ways there to be a couple among 3 members: 4C1 ways to select a couple out of 4, which will be in the committee and 6 ways to select the third remaining member (since there will be 6 members left after we select a couple out of 8 people).

56-24=32.

Hope it's clear.
_________________
Senior Manager
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 433 [0], given: 11

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

27 Dec 2012, 20:54
LM wrote:
A committee of 3 people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

A. 16
B. 24
C. 26
D. 30
E. 32

How many ways to select 3 represented couples from 4 couples? 4!/3!1! = 4
How many ways to select a person from a pair? 2
$$=4 * 2 * 2 * 2 = 32$$

More detailed explanation here : Selection/Deselection Technique
_________________

Impossible is nothing to God.

Current Student
Joined: 18 Jun 2013
Posts: 6
Location: United States
Concentration: Marketing, Strategy
GMAT 1: 540 Q39 V27
GMAT 2: 640 Q44 V35
GPA: 3.59
Followers: 0

Kudos [?]: 7 [0], given: 5

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

02 Sep 2013, 22:55
I solved it using this method, hope I'm using the correct concept

total 4 couples = 8 people in total
total no of ways to choose 3 people out of 8 = 8!/(5!3!) = 56
No. of ways couples are included in the com = 4! = 24
Therefore no. of couples with no couples included = 56-24 = 32.
Intern
Joined: 05 Oct 2013
Posts: 21
Followers: 0

Kudos [?]: 6 [0], given: 0

### Show Tags

26 Oct 2013, 18:03
schokshi99 wrote:
A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

A. 16
B. 24
C. 26
D. 30
E. 32

Because people who are married to each other cannot both serve on the committee, three members of the committee must come from 3 different couples. We have 4 ways to pick 3 couples from 4 couples. For each couple, we have 2 choices to pick one of them.
So the answer is 4 * 2 * 2 *2 = 32 (E)

Last edited by tuanle on 26 Oct 2013, 20:39, edited 2 times in total.
Intern
Joined: 29 Jan 2013
Posts: 47
Followers: 1

Kudos [?]: 38 [0], given: 24

### Show Tags

26 Oct 2013, 20:20
Agreed with Tuanle.

Another easy way is to write down all the ways to select

We have total 4 men and 4 women from which we need to form a committee of 3 such that husband and wife wont be included

The combinations are

1) MMM (all 3 men) - 4c3 = 4
2) MMW (Two men and one women) - 4c2 * 2c1 (the wives of selected men should not be included) = 12
3) WWM - 4c2*2c1 = 12
4) WWW - 4c3 = 4

Total = 4+12+12+4=32
Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7068

Kudos [?]: 92951 [0], given: 10541

### Show Tags

27 Oct 2013, 04:47
Expert's post
2
This post was
BOOKMARKED
schokshi99 wrote:
A committee of three people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?

A. 16
B. 24
C. 26
D. 30
E. 32

Merging similar topics. Please refer to the solutions provided.

Similar problems to pracitce:
a-committee-of-three-people-is-to-be-chosen-from-four-teams-130617.html
if-4-people-are-selected-from-a-group-of-6-married-couples-99055.html
a-committee-of-3-people-is-to-be-chosen-from-four-married-94068.html
if-a-committee-of-3-people-is-to-be-selected-from-among-88772.html
a-comittee-of-three-people-is-to-be-chosen-from-four-married-130475.html
a-committee-of-three-people-is-to-be-chosen-from-4-married-101784.html
a-group-of-10-people-consists-of-3-married-couples-and-113785.html
if-there-are-four-distinct-pairs-of-brothers-and-sisters-99992.html

_________________
Intern
Joined: 09 Nov 2013
Posts: 17
Location: United Arab Emirates
Concentration: Operations, Technology
Schools: MBS '16 (A)
GPA: 3.4
WE: Engineering (Energy and Utilities)
Followers: 0

Kudos [?]: 7 [0], given: 18

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

12 Nov 2013, 10:42
instead of thinking as husband and wife in the group, think of them as all different ppl in groups of two. you can only select one person from each group

so that means

(a,b) (c,d) (e,f) (g,h)

and we need to fill in 3 spaces

_ x_ x_

any one person can come from each group, so three spaces filled by one person from each group are

2x2x2 - (A)

taking different combos of the group => 4C3 => 4 - (B)

multiply (A) and (B) gives all the different ways this group can be created

(A) x (B) = 2x2x2x4 = 32 Thus choice E
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 53 [0], given: 23

### Show Tags

23 Apr 2014, 19:01
Bunuel wrote:
A committee of 3 people is to be chosen from four married couples. What is the number of different committees that can be chosen if two people who are married to each other cannot both serve on the committee?
A. 16
B. 24
C. 26
D. 30
E. 32

One of the approaches:

Each couple can send only one "representative" to the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) out of 4 to send only one "representatives" to the committee: 4C3=4.

But each of these 3 couples can send two persons (husband or wife): 2*2*2=2^3=8.

Total # of ways: 4C3*2^3=32.

Hi Bunuel, Sorry for the tedious questions.

I know this has been addressed in the other posts but still having a hard time grasping the concept, if I use the concept of 8(first choice) x6(second choice)x 4(third choice) ...why do I need to divide by 3!. Doesn't that mean that there are orders in how these members are getting chosen and we don't care for that? meaning, it's a permutation problem -- am i correct? IF it is a permutation problem, why aren't we using the traditional permutation formula of 8!/3!?

I also used another approach of (8c1)(6c1)(4c1) / (8c3). Why is that wrong?

Conversely, if I use your method listed above, I can get onboard with the "4c3" part as we need 3 different couples out of the 4 but i'm not grasping the concept of cubing "2". Shouldn't we be doing 2^4?

Thanks a ton.
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 53 [0], given: 23

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

23 Apr 2014, 19:31
Bunuel wrote:
watwazdaquestion wrote:
is this a correct way to get the answer? or was it just coincidence:

8C3 - 4(4C2) = 56 - 4(6) = 32

It's not clear what is the logic behind the formula.

Reversed approach would be:
There are 8C3=56 ways to select 3 people out of 8 without any restriction;
There are 4C1*6=24 ways there to be a couple among 3 members: 4C1 ways to select a couple out of 4, which will be in the committee and 6 ways to select the third remaining member (since there will be 6 members left after we select a couple out of 8 people).

56-24=32.

Hope it's clear.

Hi Bunuel,

I'm confused by this step, which is also outlined above. "There are 4C1*6=24 ways there to be a couple among 3 members:". Can you please elaborate on this?
Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7068

Kudos [?]: 92951 [1] , given: 10541

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

24 Apr 2014, 00:25
1
KUDOS
Expert's post
russ9 wrote:
Bunuel wrote:
watwazdaquestion wrote:
is this a correct way to get the answer? or was it just coincidence:

8C3 - 4(4C2) = 56 - 4(6) = 32

It's not clear what is the logic behind the formula.

Reversed approach would be:
There are 8C3=56 ways to select 3 people out of 8 without any restriction;
There are 4C1*6=24 ways there to be a couple among 3 members: 4C1 ways to select a couple out of 4, which will be in the committee and 6 ways to select the third remaining member (since there will be 6 members left after we select a couple out of 8 people).

56-24=32.

Hope it's clear.

Hi Bunuel,

I'm confused by this step, which is also outlined above. "There are 4C1*6=24 ways there to be a couple among 3 members:". Can you please elaborate on this?

First couple: $$A_1,A_2$$;
Second couple: $$B_1,B_2$$;
Third couple: $$C_1,C_2$$;
Fourth couple: $$D_1,D_2$$.

We want to select 3 people: a couple and one more.

We can select any from 4 couples (4 options) and for the third member we can select any from the remaining 6 people. For example if we select $$A_1,A_2$$, then we can select third member from $$B_1,B_2,C_1,C_2,D_1,D_2$$.

Hope it's clear.
_________________
Senior Manager
Joined: 15 Aug 2013
Posts: 328
Followers: 0

Kudos [?]: 53 [0], given: 23

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

24 Apr 2014, 18:12
Bunuel wrote:

First couple: $$A_1,A_2$$;
Second couple: $$B_1,B_2$$;
Third couple: $$C_1,C_2$$;
Fourth couple: $$D_1,D_2$$.

We want to select 3 people: a couple and one more.

We can select any from 4 couples (4 options) and for the third member we can select any from the remaining 6 people. For example if we select $$A_1,A_2$$, then we can select third member from $$B_1,B_2,C_1,C_2,D_1,D_2$$.

Hope it's clear.

Hi Bunuel,

I should've elaborated:

If the goal is to find combinations with NO couples, how does "total-combo of at least 1 couple" equal "no couples"? Aren't there possibilities of 2,3,4 couples?

Additionally, why wouldn't it be (4c1)(2^3)? Is this equation saying that we should chose 1 couple out of 4 and we have 3 couples left so 2*2*2?
Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7068

Kudos [?]: 92951 [0], given: 10541

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

06 May 2014, 08:06
russ9 wrote:
Bunuel wrote:

First couple: $$A_1,A_2$$;
Second couple: $$B_1,B_2$$;
Third couple: $$C_1,C_2$$;
Fourth couple: $$D_1,D_2$$.

We want to select 3 people: a couple and one more.

We can select any from 4 couples (4 options) and for the third member we can select any from the remaining 6 people. For example if we select $$A_1,A_2$$, then we can select third member from $$B_1,B_2,C_1,C_2,D_1,D_2$$.

Hope it's clear.

Hi Bunuel,

I should've elaborated:

If the goal is to find combinations with NO couples, how does "total-combo of at least 1 couple" equal "no couples"? Aren't there possibilities of 2,3,4 couples?

How there be more than one couple in 3 people?
_________________
Senior Manager
Joined: 17 Sep 2013
Posts: 394
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
Followers: 19

Kudos [?]: 270 [0], given: 139

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

18 May 2014, 21:22
No specific information on the Guys Vs Gals in the committee

3 Guys: 4C3
2 Guys 1 Girl: 4C2 * 2C1----> Choose from the girls who are not married to the 2 guys chosen already
3Girls: 4C3
2 Girls 1 Guy: 4C2 * 2C1----> Choose from the guys who are not married to the 2 girls chosen already

4+4+12+12=32
_________________

Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..

Intern
Joined: 08 May 2014
Posts: 1
Location: India
GMAT 1: 700 Q49 V34
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

01 Jul 2014, 23:49
First, let us select the couple 1,
so if H1W1 is selected there can there can be only 6 ways of choosing 1 member from the other 3 couples.
It goes the same for the other three couples.
So, if we are to select the members such that there would always be a couple in the committee then it can be done in 6 *4 ways= 24 ways.

Now we can select any 3 members from 8 persons in 8C3 =56 ways.

So no of ways of selecting members who are not couples is 56-24=32 ways
Manager
Joined: 30 Mar 2013
Posts: 137
Followers: 0

Kudos [?]: 41 [0], given: 196

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

12 Nov 2014, 22:44
8*6*4. then divide by 3! to get rid of duplicates
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13421
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

16 Nov 2015, 15:38
Hello from the GMAT Club BumpBot!

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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 23 Apr 2015
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

23 Feb 2016, 04:25
can we solve like this way

8C3 total 56 committees and now we gave to select only male combination is 4!
56 - 4! = 32
Verbal Forum Moderator
Joined: 02 Aug 2009
Posts: 4219
Followers: 325

Kudos [?]: 3442 [0], given: 100

A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

23 Feb 2016, 04:33
pkk1611 wrote:
can we solve like this way

8C3 total 56 committees and now we gave to select only male combination is 4!
56 - 4! = 32

hi,
the answer may be correct but the method/logic is not clear..
why are you subtracting male combinations?

_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Manager
Joined: 03 Dec 2014
Posts: 134
Location: India
GMAT 1: 620 Q48 V27
GPA: 1.9
WE: Engineering (Energy and Utilities)
Followers: 2

Kudos [?]: 36 [0], given: 390

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

02 Apr 2016, 11:11
shrouded1 wrote:
So there are 3 people we need to choose from 8.

Case 1 : all 3 are men ... C(4,3)=4 ways
Case 2 : all 3 are women ... C(4,3)=4 ways
Case 3 : 2 men 1 woman ... Choose men in C(4,2) ways, then we can only choose the woman in 2 ways, since their wives can't be chosen .., hence 12x2=24 ways
Case 4 : 2 women 1 man ... Exactly same logic as case 3, 12 ways

Total ways = 4+4+12+12 = 32

Posted from my mobile device

wonderful explanation . I really liked .
Manager
Joined: 25 Jun 2016
Posts: 52
Followers: 4

Kudos [?]: 21 [0], given: 4

Re: A committee of 3 people is to be chosen from four married [#permalink]

### Show Tags

25 Jun 2016, 15:37
We can solve this in two general steps.

1) We can pretend order matters (which can be much easier to visualize)
2) Then we can think about what happens if order doesn't matter.

1) If order matters, we can visualize three chairs or slots or whatever and consider them one at a time: Anybody can sit in the first chair, so there are 8 options for chair one. But now that somebody is in chair one, there are only 6 options for chair two (it can't be the person in chair one and it can't be that person's spouce). And for every set of people occupying chairs one and two, there are only 4 remaining people allowed to sit in chair three.

That means that there are 8*6*4 ways to fill the three chairs.

2) But we're looking for 'committees.' and for committees order doesn't matter (whereas it does when we're visualizing chairs). For example, Andy, Beth, Charlie would be the same committee as Beth, Andy Charlie.

In fact there are six ways that Andy Beth and Charlie could fill the chairs:

ABC
ACB
BAC
BCA
CAB
CBA

So for each committee, we counted 6 different ways for them to fill the chairs.

In other words, our 8*6*4 number is too big by a factor of 6.

Therefore, the answer is (8*6*4)/6 = 32
Re: A committee of 3 people is to be chosen from four married   [#permalink] 25 Jun 2016, 15:37

Go to page   Previous    1   2   3    Next  [ 43 posts ]

Similar topics Replies Last post
Similar
Topics:
24 A committee of three people is to be chosen from four teams 20 12 Apr 2012, 17:48
A comittee of three people is to be chosen from four married 1 09 Apr 2012, 12:55
12 A committee of three people is to be chosen from 4 married 18 18 Nov 2007, 19:15
7 A committee of three people is to be chosen from four 9 27 Sep 2009, 23:41
29 A committee of three people is to be chosen from four marrie 8 13 Nov 2007, 06:31
Display posts from previous: Sort by