by: laborumpossimus
45 mins
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included!
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (01:59) correct
21%
(02:32)
wrong
based on 428
sessions
History
Date
Time
Result
Not Attempted Yet
If a music class consists of 4 girls and 7 boys, how many ways can a group of 3 be formed if it must include at least one boy?
A. 155
B. 158
C. 161
D. 165
E. 172
A. 155
B. 158
C. 161
D. 165
E. 172
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
bmwhype2
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
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
(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
If a music class consists of 4 girls and 7 boys, how many ways can a group of 3 be formed if it must include at least one boy?
A. 155
B. 158
C. 161
D. 165
E. 172
REVERSE APPROACH:
The number of groups with at least one boy is equal to the total number of groups of 3 that can be formed from 11 students minus the groups consisting solely of girls:
\(C^3_{11}-C^3_4=161\).
DIRECT APPROACH:
The number of groups with at least one boy is the sum of the groups with one boy (and 2 girls), the groups with 2 boys (and 1 girl), and the groups with 3 boys:
\(C^1_{7}*C^2_4+C^2_{7}*C^1_4+C^3_{7}=161\).
Answer: C
_________________
A. 155
B. 158
C. 161
D. 165
E. 172
REVERSE APPROACH:
The number of groups with at least one boy is equal to the total number of groups of 3 that can be formed from 11 students minus the groups consisting solely of girls:
\(C^3_{11}-C^3_4=161\).
DIRECT APPROACH:
The number of groups with at least one boy is the sum of the groups with one boy (and 2 girls), the groups with 2 boys (and 1 girl), and the groups with 3 boys:
\(C^1_{7}*C^2_4+C^2_{7}*C^1_4+C^3_{7}=161\).
Answer: C
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Awesome. Thanks Bunuel!
Cheers,
Diana
Cheers,
Diana
JeffTargetTestPrep
Expert
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,973
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert reply
Posts: 2,973
bmwhype2
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.
Answer: C
_________________
Jeffrey Miller | Head of GMAT Instruction |
[email protected]
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
Moderator:
Announcements
Monday, Sep 14, 2026
11:30am NY / 3:30pm London / 9pm Mumbai
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.