Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions

How many different groups can be formed?

Expert replies
by CappyAA » Tue Aug 12, 2008 5:16 pm
A certain law firm consists of 4 senior partners and 6 junior partners. How many different groups of 3 partners can be formed in which at least one member of the group is a senior partner? (Two groups are considered different if at least one group member is different.)

A. 48
B. 100
C. 120
D. 288
E. 600


Thanks,
Cappy
Join the discussion
Source: — Problem Solving |

by egybs » Tue Aug 12, 2008 5:53 pm
What's the total number of groups possible?

10C3 (because there are ten total people): 10!/(7!*3!) = 120


But that includes all the cases where there are no senior partners...

So let's figure out the number of cases where there are no senior partners....

6C3 (because there are 6 junior partners) = 6!/(3!*3!) = 20

So 120 - 20 = 100 or the number of possible groups where there is at least 1 senior partner.
Join the discussion

by gracezz » Wed May 12, 2010 7:04 pm
i went for this caculation

4!*9!/(7!*2!)=144 at least have one senior, right? so 4!, and you pick two out of the rest nine persons.

would you guys tell me at what point I am wrong with the puzzle?
Join the discussion

by chocoswiss » Sun Oct 03, 2010 2:56 am
Hi

Sorry I still dont understand Why i cant do as below:
1S2J: 4*6*5
2S1J: 4*3*6
3S: 4*3*2


I somehow always end up reverting to the slot method
Join the discussion

by GMATGuruNY » Sun Oct 03, 2010 3:11 am
chocoswiss wrote:Hi

Sorry I still dont understand Why i cant do as below:
1S2J: 4*6*5
2S1J: 4*3*6
3S: 4*3*2

I somehow always end up reverting to the slot method
Since order doesn't matter, you need to do some dividing in order to account for the duplicate combinations:

1S2J = 4 * (6*5)/(1*2) = 60
2S1J = (4*3)/(1*2) * 6 = 36
3S = (4*3*2)/(1*2*3) = 4

60+36+4 = 100.

You also could use the slot method this way:

Total possible groups of 3 = (10*9*8)/(1*2*3) = 120
Total possible groups of 3 with only junior partners = (6*5*4)/(1*2*3) = 20
Total possible groups of 3 with at least 1 senior partner = 120-20 = 100.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Join the discussion