BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

What is the difference between the number of three-member

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2640
Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members
by AAPL » Wed Dec 05, 2018 5:17 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

Princeton Review

What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

OA D.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Wed Dec 05, 2018 6:48 am
AAPL wrote:Princeton Review

What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504
The number of three-member committees that can be formed from a group of nine members
Since the order in which we select the 3 people does not matter, we can use combinations.
We can choose 3 people from 9 people in 9C3 ways
9C3 = (9)(8)(7)/(3)(2)(1) = 84 three-member committees

The total number of ways there are to ARRANGE the members of such a committee
We can arrange n objects in n! ways
So, we can arrange the 3 people (in the committee) in 3! ways (= 6 ways)

DIFFERENCE = 84 - 6 = 78
78 is not among the answer choices.

hmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm!

It appears (given the official answer) that we're supposed to arrange the 3 members in each of the 84 three-member committees
So, for each of the 84 three-member committees, we can arrange the three people in 6 ways
So, the total number of arrangements = (84)(6) = 504
So, the DIFFERENCE = 504 - 84 = 420 (D)

IMO, this question is too ambiguous to be GMAT-worthy.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Wed Dec 05, 2018 1:43 pm
Hi All,

To start, I agree with Brent; the wording of this prompt is 'clunky' - and the GMAT writers word their questions in a far more rigorous and specific fashion than what we see here. That having been said, the basic concepts involved here are Combinations and Permutations.

We're asked for the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee. The intent of this question is to ask for the difference in the number of possible 3-person groups and the number of ways to arrange 3 of the 9 people 'in a row.'

For the number of 3-person groups, we can use the Combination Formula: N!/K!(N-K)! = 9!/3!(9-3)! = (9)(8)(7)/(3)(2)(1) = 504/6 = 84

The number of ways to arrange 3 of the 9 people in a row = (9)(8)(7) = 504

The difference is 504 - 84 = 420

Final Answer: D

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

by fskilnik@GMATH » Wed Dec 05, 2018 6:20 pm
[Possible alternate question stem to avoid Brent´s and Rich´s (and also my) insatisfaction]

What is the difference between the number of ways to select a three-member committee from a group of nine members, taking or not taking into account the order of selection of these members?

A. 0
B. 84
C. 252
D. 420
E. 504
$$? = 3!C\left( {9,3} \right) - C\left( {9,3} \right)\,\,\mathop = \limits^{\left( * \right)} \,\,\,84\left( {3! - 1} \right) = 5 \cdot 84 = 420$$
$$\left( * \right)\,\,\,C\left( {9,3} \right) = {{9 \cdot 8 \cdot 7} \over {3 \cdot 2}} = 3 \cdot 4 \cdot 7 = 84$$
This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8151
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Fri Mar 22, 2019 8:23 am
AAPL wrote:Princeton Review

What is the difference between the number of three-member committees that can be formed from a group of nine members and the total number of ways there are to arrange the members of such a committee?

A. 0
B. 84
C. 252
D. 420
E. 504

OA D.
The number of 3-member committees that can be formed from 9 people (i.e., order doesn't matter) is 9C3 = 9!/(3! x 6!) = (9 x 8 x 7)/3! = (9 x 8 x 7)/(3 x 2) = 3 x 4 x 7 = 84.

The number of ways to form the committees and arrange the members (i.e., order matters) is 9P3 = 9!/6! = 9 x 8 x 7 = 504.

Thus, the difference is 504 - 84 = 420.

Answer: D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1