Last visit was: 28 Apr 2026, 22:57 It is currently 28 Apr 2026, 22:57
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,963
Own Kudos:
811,842
 [6]
Given Kudos: 105,936
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,963
Kudos: 811,842
 [6]
In how many ways can 10 different paintings be distributed between two 08 Nov 2021, 07:45
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

82% (02:13) correct 18% (02:57) wrong based on 201 sessions

History

Date
Time
Result
Not Attempted Yet
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if Dave should get either three paintings or five paintings? (All paintings should be given away).

A) 120
B) 252
C) 372
D) 1092
E) 2100
ShowHide Answer
Official Answer
C
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 28 Apr 2026
Posts: 8,633
Own Kudos:
5,191
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,633
Kudos: 5,191
In how many ways can 10 different paintings be distributed between two 08 Nov 2021, 07:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
total paintings 10
For Dave to get 3 paintings 10c3 ways and 5 paintings 10c5
total ways would be 10c3+10c5 ; 120+ 252 ; 372 ways
option C

Bunuel
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if Dave should get either three paintings or five paintings? (All paintings should be given away).

A) 120
B) 252
C) 372
D) 1092
E) 2100
Show more
User avatar
IanStewart
User avatar
GMAT Tutor
Joined: 24 Jun 2008
Last visit: 24 Apr 2026
Posts: 4,143
Own Kudos:
11,285
Given Kudos: 99
Expert
Expert reply
Posts: 4,143
Kudos: 11,285
In how many ways can 10 different paintings be distributed between two 08 Nov 2021, 07:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
We're either choosing 3 paintings from the ten to give to Dave, or we're choosing 5 paintings from the 10 to give to Dave. The order of the paintings doesn't matter, so the answer is 10C5 + 10C3 = 252 + 120 = 372.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 28 Apr 2026
Posts: 109,963
Own Kudos:
811,842
Given Kudos: 105,936
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,963
Kudos: 811,842
In how many ways can 10 different paintings be distributed between two 13 Nov 2021, 01:15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if Dave should get either three paintings or five paintings? (All paintings should be given away).

A) 120
B) 252
C) 372
D) 1092
E) 2100
Show more

Veritas Prep Official Solution



There are two ways of distributing the paintings in this case:

Dave gets 3 paintings and Mona gets the rest: You select 3 of the 10 paintings and give them to Dave. This can be done in 10C3 = 120 ways

Dave gets 5 paintings and Mona gets the rest: You select 5 of the 10 paintings and give them to Dave. This can be done in 10C5 = 252 ways

Total number of ways in which you can distribute the paintings = 120 + 252 = 372 ways
User avatar
jeff564
User avatar
Joined: 19 Oct 2022
Last visit: 24 Nov 2022
Posts: 3
Own Kudos:
2
 [1]
Given Kudos: 9
Posts: 3
Kudos: 2
 [1]
In how many ways can 10 different paintings be distributed between two 18 Nov 2022, 09:57
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi, just a small question.
Why have we not calculated anything for Mona and just calculated the total possible ways for Dave as our final answer?
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 28 Apr 2026
Posts: 22,294
Own Kudos:
26,551
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,294
Kudos: 26,551
In how many ways can 10 different paintings be distributed between two 18 Nov 2022, 11:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if Dave should get either three paintings or five paintings? (All paintings should be given away).

A) 120
B) 252
C) 372
D) 1092
E) 2100
Show more


If Dave gets 5 paintings, the number of ways that can happen is:

10C5 = (10 x 9 x 8 x 7 x 6)/(5 x 4 x 3 x 2) = 3 x 2 x 7 x 6 = 252 ways

If Dave gets 3 paintings the number of ways that can happen is:

10C3 = (10 x 9 x 8)/(3 x 2) = 5 x 3 x 8 = 120 ways

So, the total 252 + 120 = 372 ways.

Answer: C
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,985
Own Kudos:
1,119
Posts: 38,985
Kudos: 1,119
In how many ways can 10 different paintings be distributed between two 05 Jun 2024, 02:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
109963 posts
Krunaal
Tuck School Moderator
852 posts