Find all School-related info fast with the new School-Specific MBA Forum

It is currently 02 Sep 2015, 03:08
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The music class consists of 4 girls and 7 boys. How many way

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
CEO
CEO
User avatar
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 421 [0], given: 4

The music class consists of 4 girls and 7 boys. How many way [#permalink] New post 16 Oct 2007, 10:50
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (02:34) correct 18% (02:17) wrong based on 206 sessions
The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?

A. 155
B. 158
C. 161
D. 165
E. 172
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2012, 03:04, edited 1 time in total.
Edited the question.
VP
VP
avatar
Joined: 10 Jun 2007
Posts: 1463
Followers: 6

Kudos [?]: 153 [0], given: 0

Re: PS Combinatorics - Music Class [#permalink] New post 16 Oct 2007, 11:02
1
This post was
BOOKMARKED
bmwhype2 wrote:
The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?

155
158
161
165
172


Classic combination problem
At least 1 boy = Total - all girls
All girls = C(4,3) = 4
Total combination = C(11,3) = 165
Ans = 165-4 = 161
1 KUDOS received
Manager
Manager
avatar
Joined: 19 Aug 2007
Posts: 170
Followers: 1

Kudos [?]: 23 [1] , given: 0

 [#permalink] New post 16 Oct 2007, 11:11
1
This post received
KUDOS
Case 1: All three boys
(7 choose 3) = 35

Case 2: Two boys, one girl
(7 choose 2) * (4 choose 1) = 84

Case 3: One boy, two girls
(7 choose 1) * (4 choose 2) = 42


Add them up 35 + 84 + 42 = 161
C
Intern
Intern
avatar
Joined: 25 Jun 2011
Posts: 49
Location: Sydney
Followers: 0

Kudos [?]: 1 [0], given: 7

Re: [#permalink] New post 29 Jun 2012, 12:47
jimjohn wrote:
Case 1: All three boys
(7 choose 3) = 35

Case 2: Two boys, one girl
(7 choose 2) * (4 choose 1) = 84

Case 3: One boy, two girls
(7 choose 1) * (4 choose 2) = 42


Add them up 35 + 84 + 42 = 161
C


I don't really understand how Case 2 and 3 above are calculated. Any help please?


Thanks,
Diana
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29186
Followers: 4737

Kudos [?]: 50071 [0], given: 7527

Re: Re: [#permalink] New post 30 Jun 2012, 03:03
Expert's post
1
This post was
BOOKMARKED
dianamao wrote:
jimjohn wrote:
Case 1: All three boys
(7 choose 3) = 35

Case 2: Two boys, one girl
(7 choose 2) * (4 choose 1) = 84

Case 3: One boy, two girls
(7 choose 1) * (4 choose 2) = 42


Add them up 35 + 84 + 42 = 161
C


I don't really understand how Case 2 and 3 above are calculated. Any help please?


Thanks,
Diana


The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
A. 155
B. 158
C. 161
D. 165
E. 172

Reverse Approach:

The # of groups with at least one boy equal to total groups of 3 that can be formed out of 11 people minus groups with all girls: \(C^3_{11}-C^3_4=161\).

Answer: C.

Direct Approach:

The # of groups with at least one boy equal to groups with one boy (and 2 girls) plus groups with 2 boys (and 1 girl) plus groups with 3 boys: \(C^1_{7}*C^2_4+C^2_{7}*C^1_4+C^3_{7}=161\).

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 25 Jun 2011
Posts: 49
Location: Sydney
Followers: 0

Kudos [?]: 1 [0], given: 7

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink] New post 30 Jun 2012, 03:50
Awesome. Thanks Bunuel!

Cheers,
Diana
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 2046
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 32

Kudos [?]: 345 [0], given: 355

GMAT ToolKit User
Re: The music class consists of 4 girls and 7 boys. How many way [#permalink] New post 30 Dec 2013, 06:34
bmwhype2 wrote:
The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?

A. 155
B. 158
C. 161
D. 165
E. 172


Reverse combinatorics approach is preferred method on this one
Note that at least 1 boy gives clue to using this method

All combinations - four girls = answer

All combinations is 11C3 = 165

All girls 4C3 = 4

So our answer is 165-4 = 161

Hence, answer is (C)

Hope it helps
Cheers!

J :)
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6174
Followers: 344

Kudos [?]: 70 [0], given: 0

Premium Member
Re: The music class consists of 4 girls and 7 boys. How many way [#permalink] New post 29 Mar 2015, 09:08
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

Expert Post
Optimus Prep Instructor
User avatar
Joined: 06 Nov 2014
Posts: 494
Followers: 6

Kudos [?]: 93 [0], given: 2

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink] New post 31 Mar 2015, 11:47
Expert's post
bmwhype2 wrote:
The music class consists of 4 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?

A. 155
B. 158
C. 161
D. 165
E. 172


We want At least 1 boy = Total - all girls
Now all 3 girls can be selected in 4C3 = 4 ways
No. of ways in which 3 people can be selected out of 11 = !!C3 = 165
Required number of ways = 165 - 4
= 161.

--
Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
_________________

Cassandra Wolff
Customer Support | Optimus Prep
 
Facebook Linkedin Youtube Twitter slideshare Google+
 

Intern
Intern
avatar
Joined: 26 Oct 2014
Posts: 9
Followers: 0

Kudos [?]: 2 [0], given: 4

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink] New post 31 Mar 2015, 12:13
I often confuse distinct between n!/((n-k)!*k!) and simple n!/(n-k)!. In this case I spend 90 seconds using solving 3 components, got answer 420, find out that it s wrong and divided every component to k!. And I did it with a simple example (how many variants to take 2 from 4) That is not good, I suppose) Too much time, and big risk to make mistake. What can you advice?
Re: The music class consists of 4 girls and 7 boys. How many way   [#permalink] 31 Mar 2015, 12:13
    Similar topics Author Replies Last post
Similar
Topics:
3 A class consists of 5 boys and 4 girls. Given that one kid can only ho reto 6 06 Jul 2015, 09:31
6 Experts publish their posts in the topic In how many ways can 5 boys and 3 girls be seated on 8 voodoochild 5 24 Sep 2012, 12:02
35 Experts publish their posts in the topic The ratio of boys to girls in Class A is 3 to 4. The ratio changhiskhan 29 03 Apr 2010, 11:57
4 Experts publish their posts in the topic If a choir consists of 5 boys and 6 girls, in how many ways can the IrinaOK 10 10 Oct 2007, 22:36
8 Experts publish their posts in the topic In how many ways 5 boys and 6 girls can be seated on 12 ps_dahiya 11 22 Jan 2006, 00:44
Display posts from previous: Sort by

The music class consists of 4 girls and 7 boys. How many way

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.