NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 22:59 It is currently 24 Apr 2024, 22:59
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

At a dance there are four married couples: Ann and Andy, Betty and Bor

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92900
Own Kudos [?]: 618856 [15]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink] New post   17 Jan 2021, 09:12
15
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

95% (hard)

Question Stats:

33% (02:03) correct 67% (02:08) wrong based on 73 sessions
Hide Show timer Statistics
At a dance there are four married couples: Ann and Andy, Betty and Boris, Danielle and Dan, and Elaine and Eric. The wives select a husband at random with whom to share a dance. What is the probability that each of the four men dances with a woman other than his spouse?

A. 1/8
B. 1/6
C. 1/4
D. 1/3
E. 9/24

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
ShowHide Answer
Official Answer
E
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11172
Own Kudos [?]: 31896 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink] New post   17 Jan 2021, 10:33
Expert Reply
Bunuel wrote:
At a dance there are four married couples: Ann and Andy, Betty and Boris, Danielle and Dan, and Elaine and Eric. The wives select a husband at random with whom to share a dance. What is the probability that each of the four men dances with a woman other than his spouse?

A. 1/8
B. 1/6
C. 1/4
D. 1/3
E. 9/24



This is a derangement question, that is questions where none element is in its original position.
Direct formula for n elements = \(n!(\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}....+\frac{1}{n!})\)
Here n = 4 => \(4!(\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!})\)
\((\frac{4!}{2!}-\frac{4!}{3!}+\frac{4!}{4!})=12-4+1=9\)

Total ways .. First lady can choose in 4 ways, the next in 3 ways and so on => 4*3*2*1=24

P = 9/24

E
avatar
B
HamedATX
Intern
Intern
Joined: 16 Jul 2019
Posts: 9
Own Kudos [?]: 15 [0]
Given Kudos: 50
Send PM
At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink] New post   17 Jan 2021, 22:02
Bunuel wrote:
At a dance there are four married couples: Ann and Andy, Betty and Boris, Danielle and Dan, and Elaine and Eric. The wives select a husband at random with whom to share a dance. What is the probability that each of the four men dances with a woman other than his spouse?

A. 1/8
B. 1/6
C. 1/4
D. 1/3
E. 9/24

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions


I think the answer is A=1/8.
The total number of ways 4 women can dance with the 4 men is 4!=24 and there is only 3 ways that none of the 4 wives won't dance with her souse. So the answer is 3/24 = 1/8
User avatar
P
TheGraceful
Senior Manager
Senior Manager
Joined: 10 Apr 2018
Posts: 342
Own Kudos [?]: 200 [2]
Given Kudos: 217
Concentration: Leadership, Strategy
Schools: Booth Wharton Kellogg LBS '24 INSEAD Jan'24 intake
GMAT 1: 600 Q44 V28
GPA: 3.56
WE:Engineering (Computer Software)
Send PM
Reviews Badge
Re: At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink] New post   26 Aug 2022, 07:35
2
Kudos
HamedATX wrote:
I think the answer is A=1/8.
The total number of ways 4 women can dance with the 4 men is 4!=24 and there is only 3 ways that none of the 4 wives won't dance with her souse. So the answer is 3/24 = 1/8


There are 3 options and 3 ways that none of the 4 wives won't dance with her souse. So the answer is 3*3/24 = 9/24.
User avatar
B
gmatpro15
Manager
Manager
Joined: 09 Aug 2022
Posts: 86
Own Kudos [?]: 22 [0]
Given Kudos: 48
Location: India
Concentration: General Management, Leadership
GPA: 4
WE:Design (Real Estate)
Send PM
Re: At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink] New post   26 Aug 2022, 08:08
chetan2u wrote:
Bunuel wrote:
At a dance there are four married couples: Ann and Andy, Betty and Boris, Danielle and Dan, and Elaine and Eric. The wives select a husband at random with whom to share a dance. What is the probability that each of the four men dances with a woman other than his spouse?

A. 1/8
B. 1/6
C. 1/4
D. 1/3
E. 9/24



This is a derangement question, that is questions where none element is in its original position.
Direct formula for n elements = \(n!(\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}....+\frac{1}{n!})\)
Here n = 4 => \(4!(\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!})\)
\((\frac{4!}{2!}-\frac{4!}{3!}+\frac{4!}{4!})=12-4+1=9\)

Total ways .. First lady can choose in 4 ways, the next in 3 ways and so on => 4*3*2*1=24

P = 9/24

E




Can you ellobarate the formula?

Posted from my mobile device
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32659
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink] New post   28 Mar 2024, 10:50
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.
GMAT Club Bot
gmatclubot
Re: At a dance there are four married couples: Ann and Andy, Betty and Bor [#permalink]
28 Mar 2024, 10:50
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions