Last visit was: 24 Apr 2026, 14:38 It is currently 24 Apr 2026, 14:38
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
805+ (Hard)|   Combinations|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,068
 [18]
Given Kudos: 105,873
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: 109,818
Kudos: 811,068
 [18]
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 09 Oct 2020, 03:15
1
Kudos
Add Kudos
17
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:

95% (hard)

Question Stats:

33% (02:35) correct 67% (02:05) wrong based on 178 sessions

History

Date
Time
Result
Not Attempted Yet
Rick’s Sandwich Shop lets customers create their own sandwiches by choosing from among a certain number of ingredients. When ordering Rick’s Rockin’ Sandwich, the customer must choose 1 of 3 breads, 1 of 6 meats, and 1 of 4 cheeses. The customer can also add up to 3 of 8 different veggies. How many unique Rick’s Rockin’ Sandwiches could a customer order?


A. 4,032

B. 6,624

C. 6,696

D. 24,192

E. 28,932
ShowHide Answer
Official Answer
C
Most Helpful Reply
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 24 Apr 2026
Posts: 8,629
Own Kudos:
5,190
 [5]
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: 8,629
Kudos: 5,190
 [5]
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 09 Oct 2020, 03:59
5
Kudos
Add Kudos
Bookmarks
Bookmark this Post
must choose
breads 3c1 ; 3
meats 6c1 ; 6
cheeses 4c1 ; 4
veggies can also be added condition ( conditional ) (0,1,2,3)
we get 4 cases
no veggies ;3*6*4 ; 72
1 veggie ; 72*8 ; 576
2 veggies ; 72*8c2 ; 2016
3 veggies ; 72* 8c3 ; 4032
total possiblities ; 72 +576+2016+4032 ; 6696
option C

Bunuel
Rick’s Sandwich Shop lets customers create their own sandwiches by choosing from among a certain number of ingredients. When ordering Rick’s Rockin’ Sandwich, the customer must choose 1 of 3 breads, 1 of 6 meats, and 1 of 4 cheeses. The customer can also add up to 3 of 8 different veggies. How many unique Rick’s Rockin’ Sandwiches could a customer order?


A. 4,032

B. 6,624

C. 6,696

D. 24,192

E. 28,932
Show more
General Discussion
User avatar
logro
User avatar
Joined: 15 Oct 2017
Last visit: 21 Nov 2021
Posts: 322
Own Kudos:
181
 [1]
Given Kudos: 52
WE:Investment Banking (Finance: Investment Banking)
Products:
My Reviews
Posts: 322
Kudos: 181
 [1]
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 09 Oct 2020, 03:21
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Total number of ways = 3C1*6C1*4C1*8C3 = 3*6*4*56 = 4032

Hence it's A
User avatar
MathRevolution
User avatar
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Last visit: 27 Sep 2022
Posts: 10,063
Own Kudos:
20,001
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Expert
Expert reply
GMAT 1: 760 Q51 V42
Posts: 10,063
Kudos: 20,001
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 09 Oct 2020, 03:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total number of ways: \(^3{C_1} * ^4{C_1} * ^6{C_1} * ^8{C_3}\)

=> 3 * 4 * 6 * 56

=> 4,032

Answer A
avatar
cherr012
avatar
Joined: 16 Jul 2020
Last visit: 23 Jul 2021
Posts: 14
Own Kudos:
4
 [1]
Given Kudos: 73
Schools: LBS MiM "22 HEC MiM "23 INSEAD MiM "22 Imperial MFin "22 ESSEC MiM "23 SMU MiM Jul "22 NUS MiM "21
Schools: LBS MiM "22 HEC MiM "23 INSEAD MiM "22 Imperial MFin "22 ESSEC MiM "23 SMU MiM Jul "22 NUS MiM "21
Posts: 14
Kudos: 4
 [1]
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 09 Oct 2020, 03:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[quote="MathRevolution"]Total number of ways: \(^3{C_1} * ^4{C_1} * ^6{C_1} * ^8{C_3}\)

=> 3 * 4 * 6 * 56

=> 4,032

Here it is mentioned upto 3 which according to me means that the sandwich can have 0-3 choices of veggies , doesn't it?

Posted from my mobile device
User avatar
Praveenksinha
User avatar
Joined: 11 Apr 2018
Last visit: 08 Jul 2021
Posts: 105
Own Kudos:
107
 [1]
Given Kudos: 298
Location: India
Concentration: Entrepreneurship, Marketing
GPA: 3.7
WE:Sales (Energy)
Products:
My Reviews
Posts: 105
Kudos: 107
 [1]
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 09 Oct 2020, 05:33
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel I didn't get why A is correct. For veggies a person can choose up to 3 veggies, it can be 0,1,2 or 3. Please help why 8C3 is correct.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,818
Own Kudos:
811,068
Given Kudos: 105,873
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: 109,818
Kudos: 811,068
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 12 Oct 2020, 05:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Rick’s Sandwich Shop lets customers create their own sandwiches by choosing from among a certain number of ingredients. When ordering Rick’s Rockin’ Sandwich, the customer must choose 1 of 3 breads, 1 of 6 meats, and 1 of 4 cheeses. The customer can also add up to 3 of 8 different veggies. How many unique Rick’s Rockin’ Sandwiches could a customer order?


A. 4,032

B. 6,624

C. 6,696

D. 24,192

E. 28,932
Show more

Anyone else wants to try?
User avatar
yashikaaggarwal
User avatar
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Last visit: 29 Mar 2026
Posts: 3,089
Own Kudos:
3,158
Given Kudos: 1,510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Schools: Cranfield (A) Warwick MiM "23 (M)
Posts: 3,089
Kudos: 3,158
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 12 Oct 2020, 05:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Meat, Bread and Cheeses can be selected in 6C1*3C1*4C1 = 72 ways
Veggies portion is Optional.
Anyone can include veggies in their sandwiches up to 3 options out of 8

Let say there are 4 persons
=> A want sandwich with all 3 veggies kind
=> B want sandwich with 2 veggies kind
=> C want sandwich with only 1 veggie kind
=> D want sandwich with No Veggie

=> A can take sandwich in 8C3*72 = 4032 ways
=> B can take sandwich in 8C2*72 = 2016 ways
=> C can take sandwich in 8C1*72 = 576 ways
=> D can take sandwich in 8C0*72 = 72 ways (8C0 = 1)

Total ways = 4032+2016+576+72 = 6696 ways.

Answer is C

Posted from my mobile device
User avatar
Neha2404
User avatar
Joined: 07 Mar 2020
Last visit: 27 Oct 2025
Posts: 118
Own Kudos:
52
 [1]
Given Kudos: 78
Location: India
Concentration: Finance, Accounting
Schools: IIMA PGPX'22 ISB'22 IIMB EPGP'22 Kellogg '22
Schools: IIMA PGPX'22 ISB'22 IIMB EPGP'22 Kellogg '22
Posts: 118
Kudos: 52
 [1]
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 12 Oct 2020, 05:54
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
IMO- C
In this question
Choose of veggies is optional
Customer can choose veggies in 4 ways
No veggies- 3C1*6C1*4C1*8C0. =72
1 veggies - 3C1*6C1*4C1*8C1 =576
2 veggies- 3C1*6C1*4C1*8C2. =2016
3 veggies- 3C1*6C1*4C1*8C3. =4032
Total ways. To select a sandwich. =72+576+2016+4032
=6696

Posted from my mobile device
User avatar
navderm
User avatar
Joined: 30 May 2019
Last visit: 26 May 2023
Posts: 146
Own Kudos:
31
Given Kudos: 331
Location: United States
Concentration: Technology, Strategy
GMAT 1: 700 Q49 V35
GPA: 3.6
GMAT 1: 700 Q49 V35
Posts: 146
Kudos: 31
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 12 Oct 2020, 15:52
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Rick’s Sandwich Shop lets customers create their own sandwiches by choosing from among a certain number of ingredients. When ordering Rick’s Rockin’ Sandwich, the customer must choose 1 of 3 breads, 1 of 6 meats, and 1 of 4 cheeses. The customer can also add up to 3 of 8 different veggies. How many unique Rick’s Rockin’ Sandwiches could a customer order?


A. 4,032

B. 6,624

C. 6,696

D. 24,192

E. 28,932
Show more


Doing any calculation more than needed is a waste of time here.

We know that there are 3C1 ways of choosing the bread, 6C1 ways of choosing the meats, and 4C1 ways of choosing the cheese.
So that makes 3 * 6 * 4 = 72

Now, we can choose 0, 1, 2, or 3 of the 8 vegetables.
That is (8C0 + 8C1 + 8C2 + 8C3) = 93

Since one of the aforementioned combinations of vegetables will always be chosen with the calculated combination of bread, meats, and cheese.
it's 72 * 93

Looking at ones place of both those numbers, 2 * 3 = 6. Only C has 6 in it's unit place.
So, C
avatar
tleknight
avatar
Joined: 19 Nov 2019
Last visit: 25 Oct 2021
Posts: 4
Own Kudos:
1
Given Kudos: 5
Posts: 4
Kudos: 1
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 27 Oct 2020, 22:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
= [3C1*6C1*4C1] x [8C0+8C1+8C2+8C3]
= 72 x 93
= 6696
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,974
Own Kudos:
1,117
Posts: 38,974
Kudos: 1,117
Rick’s Sandwich Shop lets customers create their own sandwiches by cho 20 Nov 2024, 06:26
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
109818 posts
Krunaal
Tuck School Moderator
853 posts