It is currently 17 Oct 2017, 02:58
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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 Workbook Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

In how many ways can a group of 3 people be selected

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Intern
Intern
avatar
Joined: 07 Nov 2012
Posts: 13

Kudos [?]: 37 [0], given: 10

In how many ways can a group of 3 people be selected [#permalink]

Show Tags

New post 09 Nov 2012, 10:59
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:11) correct 25% (01:33) wrong based on 68 sessions

HideShow timer Statistics

In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225
[Reveal] Spoiler: OA

Kudos [?]: 37 [0], given: 10

1 KUDOS received
Intern
Intern
avatar
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 47

Kudos [?]: 33 [1], given: 4

Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86
Re: In how many ways can a group of 3 people be selected [#permalink]

Show Tags

New post 09 Nov 2012, 13:12
1
This post received
KUDOS
Since the question stem asks for 2 members of the same gender we get the following:
1. 2-Men and 1-Woman, hence (2C5)*(1C7) = 5*2*7=70
2. 2-Women and 1-Man, hence (2C7)*(1C5) = 7*3*5 =105
Thus, the total number of ways would be: 70+105=175

Please, correct me, if I went awry
_________________

God loves the steadfast.

Kudos [?]: 33 [1], given: 4

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128511 [2], given: 12179

Premium Member CAT Tests
Top Member of the Month
Re: In how many ways can a group of 3 people be selected [#permalink]

Show Tags

New post 10 Nov 2012, 04:48
2
This post received
KUDOS
Expert's post
derekgmat wrote:
In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225


Alternatively one can do:
The total number of committees of 3 possible out of 12 people without restrictions: \(C^3_{12}=220\);
The number of committees with all men: \(C^3_5=10\);
The number of committees with all women: \(C^3_7=35\);

Thus the answer is 220-(10+35)=175.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128511 [2], given: 12179

Manager
Manager
avatar
Joined: 28 Feb 2012
Posts: 115

Kudos [?]: 52 [0], given: 17

Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
GMAT ToolKit User
Re: In how many ways can a group of 3 people be selected [#permalink]

Show Tags

New post 12 Nov 2012, 01:45
Bunuel wrote:
derekgmat wrote:
In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225


Alternatively one can do:
The total number of committees of 3 possible out of 12 people without restrictions: \(C^3_{12}=220\);
The number of committees with all men: \(C^3_5=10\);
The number of committees with all women: \(C^3_7=35\);

Thus the answer is 220-(10+35)=175.

Answer: D.


To make this question clearer, i think it should be stated more precisely "exactly 2 of them are of the same gender" otherwise one could understand that commetees consisting of just men and/or just women are possible. Don't you think so Bunuel?
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Kudos [?]: 52 [0], given: 17

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 459

Kudos [?]: 540 [0], given: 11

Concentration: Marketing, Finance
Schools: Full Time MBA (A)
GPA: 3.23
GMAT ToolKit User
Re: In how many ways can a group of 3 people be selected [#permalink]

Show Tags

New post 28 Dec 2012, 05:05
derekgmat wrote:
In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225


M M W = \(=\frac{5!}{2!3!} * \frac{7!}{6!1!} = 10 * 7 = 70\)
W W M = \(=\frac{7!}{2!5!} * \frac{5!}{1!4!} = 21 * 5 = 105\)

\(70 + 105 = 175\)

Answer: D
_________________

Impossible is nothing to God.

Kudos [?]: 540 [0], given: 11

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16764

Kudos [?]: 273 [0], given: 0

Premium Member
Re: In how many ways can a group of 3 people be selected [#permalink]

Show Tags

New post 01 Sep 2016, 03:32
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Re: In how many ways can a group of 3 people be selected   [#permalink] 01 Sep 2016, 03:32
Print view
First unread post
Display posts from previous: Sort by

In how many ways can a group of 3 people be selected

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: Bunuel, Vyshak, Engr2012, mikemcgarry, Abhishek009, VeritasPrepKarishma, Skywalker18, msk0657, abhimahna

Search for:


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions