BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Probablity

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 468
Joined: Mon Jul 25, 2011 10:20 pm
Thanked: 29 times
Followed by:4 members

Probablity

by vipulgoyal » Tue Mar 19, 2013 3:03 am
IN HOW MANY WAYS CAN U SELECT A COMMETTEE OF 4 PEOPLE FROM A GROUP OF 5 COUPLES SO THAT NO COUPLE IS CHOSEN?

Ans given in source 80

my ans 1920
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 511
Joined: Wed Aug 11, 2010 9:47 am
Location: Delhi, India
Thanked: 344 times
Followed by:86 members

by Anju@Gurome » Tue Mar 19, 2013 3:21 am
vipulgoyal wrote:IN HOW MANY WAYS CAN U SELECT A COMMETTEE OF 4 PEOPLE FROM A GROUP OF 5 COUPLES SO THAT NO COUPLE IS CHOSEN?
Each couple can send only one "representative" to the committee.
Now, number of ways to select 4 couples (as there should be 4 members) who will send only one "representative" to the committee out of 5 couples = 5C4 = 5

Each of these 4 chosen couples can send two persons, either the husband or the wife
Hence, for each of the above combinations, number of possible combinations are = 2*2*2*2 = 16

Hence, number of ways to choose 4 people out 5 couples so that no couple is chosen = 5*16 = 80
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Top
Master | Next Rank: 500 Posts
Posts: 468
Joined: Mon Jul 25, 2011 10:20 pm
Thanked: 29 times
Followed by:4 members

by vipulgoyal » Tue Mar 19, 2013 4:20 am
Thanks, very helpful post as always
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Tue Mar 19, 2013 9:50 am
vipulgoyal wrote:IN HOW MANY WAYS CAN U SELECT A COMMETTEE OF 4 PEOPLE FROM A GROUP OF 5 COUPLES SO THAT NO COUPLE IS CHOSEN?
An alternate approach:
Number of options for the first person = 10. (Any of the 10 people.)
Number of options for the second person = 8. (Of the 9 remaining people, anyone but the mate of 1 person already chosen.)
Number of options for the third person = 6. (Of the 8 remaining people, anyone but the mates of 2 people already chosen.)
Number of options for the fourth person = 4. (Of the 7 remaining people, anyone but the mates of the 3 people already chosen.)
To combine these options, we multiply:
10*8*6*4.
Since the order of the selections doesn't matter -- ABCD is the same committee as BDAC -- we divide by the number of ways to ARRANGE the 4 people (4!):
(10*8*6*4)/(4*3*2*1) = 80.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1