Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 14:38

### 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 three people is to be chosen from four marrie

Author Message
TAGS:

### Hide Tags

Manager
Joined: 01 Nov 2007
Posts: 69
Followers: 1

Kudos [?]: 9 [2] , given: 0

A committee of three people is to be chosen from four marrie [#permalink]

### Show Tags

13 Nov 2007, 07:31
2
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:01) correct 36% (01:29) wrong based on 327 sessions

### HideShow timer Statistics

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-committee-of-3-people-is-to-be-chosen-from-four-married-94068.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Oct 2013, 01:29, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manager
Joined: 25 Jul 2007
Posts: 108
Followers: 1

Kudos [?]: 22 [1] , given: 0

### Show Tags

13 Nov 2007, 07:41
1
KUDOS

The committee could have

0 men and 3 women = 4 possibilities ( 4c3 )
1 man and 2 women = 12 possibilities ( no couple should be in the team : 4 * 3c2 )
2 men and 1 woman = 12 possibilities ( no couple should be in the team : 4c2 *2c1 )
3 men and 0 women = 4 possibilities ( 4c3 )

Therefore 4+12+12+4=32 possible teams.
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 573

Kudos [?]: 3975 [1] , given: 360

### Show Tags

09 Dec 2007, 07:08
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
E.

N=4C3*2C1*2C1*2C1=4*2*2*2=32

4C3 - 3 couples from 4 couples
2C1 - a man or woman from a couple.
Director
Joined: 01 May 2007
Posts: 793
Followers: 2

Kudos [?]: 330 [6] , given: 0

### Show Tags

09 Dec 2007, 12:29
6
KUDOS
3
This post was
BOOKMARKED
Another way to look at this is the Manhattan GMAT technique. For a restriction problem like this you want to look at it in two parts:

Total Possible Combos - Restricted Combos.

So total possible without any restrictions is:

8!/(3!)(5!) = 56 total possibilities

Now you look at the restrictions. What is the restriction -- a couple can't be together. How many are restricted? When looking at a restriction it is best to look at them as a total unit. So 1 couple is a unit. We have four couples. How can we arrange this 4 units? 4*3*2*1 = 24 combos restricted.

Manager
Joined: 10 Jul 2009
Posts: 127
Location: Ukraine, Kyiv
Followers: 4

Kudos [?]: 154 [0], given: 60

### Show Tags

07 Sep 2009, 10:36
The same as here ps-combinatorics-m02q05-55472.html
_________________

Never, never, never give up

Manager
Joined: 27 Oct 2008
Posts: 185
Followers: 2

Kudos [?]: 150 [1] , given: 3

### Show Tags

28 Sep 2009, 04:11
1
KUDOS
A committee of three people is to be chosen from four 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

1. 16
2. 24
3. 26
4. 30
5. 32

Ans: 8 * 6 * 4/3!

32 ways..

Ans is option 5
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1335
Followers: 17

Kudos [?]: 254 [1] , given: 10

### Show Tags

02 May 2011, 23:05
1
KUDOS
8*6*4 = total ways
3! is the number of permutations of 3 people.

hence 24*8/6 = 32
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15431
Followers: 649

Kudos [?]: 207 [0], given: 0

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

### Show Tags

30 Sep 2013, 12:52
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38858
Followers: 7727

Kudos [?]: 106044 [5] , given: 11607

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

### Show Tags

01 Oct 2013, 01:31
5
KUDOS
Expert's post
3
This post was
BOOKMARKED
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

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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-committee-of-3-people-is-to-be-chosen-from-four-married-94068.html

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
_________________
Re: A committee of three people is to be chosen from four marrie   [#permalink] 01 Oct 2013, 01:31
Similar topics Replies Last post
Similar
Topics:
24 A committee of three people is to be chosen from four teams 20 10 Mar 2016, 04:47
A comittee of three people is to be chosen from four married 1 09 Apr 2012, 14:08
18 A committee of three people is to be chosen from 4 married 19 21 Mar 2017, 09:30
131 A committee of 3 people is to be chosen from four married 46 20 May 2017, 20:35
7 A committee of three people is to be chosen from four 9 06 Aug 2012, 11:19
Display posts from previous: Sort by