It is currently 13 Dec 2017, 12:54

# Decision(s) Day!:

CHAT Rooms | Ross R1 | Kellogg R1 | Darden R1 | Tepper R1

### 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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

CEO
Joined: 21 Jan 2007
Posts: 2734

Kudos [?]: 1089 [0], given: 4

Location: New York City
The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

16 Oct 2007, 10:50
6
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

80% (01:28) correct 20% (02:20) wrong based on 351 sessions

### HideShow timer Statistics

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.

Kudos [?]: 1089 [0], given: 4

VP
Joined: 10 Jun 2007
Posts: 1431

Kudos [?]: 387 [1], given: 0

Re: PS Combinatorics - Music Class [#permalink]

### Show Tags

16 Oct 2007, 11:02
1
KUDOS
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

Kudos [?]: 387 [1], given: 0

Manager
Joined: 19 Aug 2007
Posts: 166

Kudos [?]: 68 [2], given: 0

### Show Tags

16 Oct 2007, 11:11
2
KUDOS
1
This post was
BOOKMARKED
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

Kudos [?]: 68 [2], given: 0

Intern
Joined: 25 Jun 2011
Posts: 47

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

Location: Sydney

### Show Tags

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

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

Math Expert
Joined: 02 Sep 2009
Posts: 42583

Kudos [?]: 135533 [1], given: 12697

### Show Tags

30 Jun 2012, 03:03
1
KUDOS
Expert's post
2
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: $$C^3_{11}-C^3_4=161$$.

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: $$C^1_{7}*C^2_4+C^2_{7}*C^1_4+C^3_{7}=161$$.

_________________

Kudos [?]: 135533 [1], given: 12697

Intern
Joined: 25 Jun 2011
Posts: 47

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

Location: Sydney
Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

30 Jun 2012, 03:50
Awesome. Thanks Bunuel!

Cheers,
Diana

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

Current Student
Joined: 06 Sep 2013
Posts: 1965

Kudos [?]: 759 [0], given: 355

Concentration: Finance
Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

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

Kudos [?]: 759 [0], given: 355

Non-Human User
Joined: 09 Sep 2013
Posts: 14869

Kudos [?]: 287 [0], given: 0

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

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.
_________________

Kudos [?]: 287 [0], given: 0

SVP
Joined: 06 Nov 2014
Posts: 1903

Kudos [?]: 549 [0], given: 23

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

31 Mar 2015, 11:47
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

Kudos [?]: 549 [0], given: 23

Intern
Joined: 26 Oct 2014
Posts: 16

Kudos [?]: 21 [0], given: 12

Location: Russian Federation
Concentration: Finance, Technology
Schools: Stanford '19 (S)
GMAT 1: 720 Q51 V36
GPA: 2.9
WE: Project Management (Retail Banking)
Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

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?

Kudos [?]: 21 [0], given: 12

Non-Human User
Joined: 09 Sep 2013
Posts: 14869

Kudos [?]: 287 [0], given: 0

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

19 Jul 2016, 04:40
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.
_________________

Kudos [?]: 287 [0], given: 0

Intern
Joined: 25 Sep 2017
Posts: 2

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

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

25 Sep 2017, 04:19
music class
4 girls
7 boys
total = 11
3 is the number of group to be formed

using this formula: n!(n-r!)r! therefore 11! - 7!
- (11-3!)3! (7-3!)3!

= 165 - 4 = 161

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

Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1802

Kudos [?]: 981 [0], given: 5

Re: The music class consists of 4 girls and 7 boys. How many way [#permalink]

### Show Tags

26 Sep 2017, 15:25
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 can determine the number of ways a group of 3 that includes at least 1 boy can be formed from 4 girls and 7 boys using the following formula:

Total number of ways to form a group of 3 - number of ways to form the group with no boys

Total number of ways to form a group of 3 is 11C3 = 11!/[3!(11-3)!] = (11 x 10 x 9)/3! = (11 x 10 x 9)/(3 x 2 x 1) = 11 x 5 x 3 = 165

Number of ways to form the group with no boys = 4C3 = 4!/[3!(4-3)!] = (4 x 3 x 2)/3! = 4

Thus, the total number of ways to select the group with at least 1 boy is 165 - 4 = 161.

_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 981 [0], given: 5

Re: The music class consists of 4 girls and 7 boys. How many way   [#permalink] 26 Sep 2017, 15:25
Display posts from previous: Sort by

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

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

 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®.