Last visit was: 24 Apr 2026, 09:05 It is currently 24 Apr 2026, 09:05
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
Patronus
User avatar
Joined: 21 Aug 2014
Last visit: 10 Nov 2016
Posts: 101
Own Kudos:
1,005
 [37]
Given Kudos: 49
Schools: Tepper '18 (WL) Krannert '18 (A) Kelley '18 (M) Simon '18 (WA) Fisher '18 (WD)
GMAT 1: 610 Q49 V25
GMAT 2: 730 Q50 V40
Schools: Tepper '18 (WL) Krannert '18 (A) Kelley '18 (M) Simon '18 (WA) Fisher '18 (WD)
GMAT 2: 730 Q50 V40
Posts: 101
Kudos: 1,005
 [37]
A restaurant serves 6 varieties of appetizers, 10 different entrees an 24 Jun 2015, 10:42
9
Kudos
Add Kudos
28
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

85% (01:37) correct 15% (01:58) wrong based on 492 sessions

History

Date
Time
Result
Not Attempted Yet
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,028
 [6]
Given Kudos: 105,871
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: 109,814
Kudos: 811,028
 [6]
A restaurant serves 6 varieties of appetizers, 10 different entrees an 24 Jun 2015, 10:50
3
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Patronus
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)
Show more


1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\);
1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\).

Total = A.

Answer: A.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,028
 [5]
Given Kudos: 105,871
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: 109,814
Kudos: 811,028
 [5]
A restaurant serves 6 varieties of appetizers, 10 different entrees an 24 Jun 2015, 11:03
3
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Patronus
Bunuel
Patronus
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)


1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\);
1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\).

Total = A.

Answer: A.
Thank you for the short answer Bunuel.

Can you please tell me why we should use \(\frac{(10*9)}{2}\) and not 10*9?
I solved it by thinking we have to fill 2 spots out of 10 contenders (entrees). Therefore, first spot can be filled in 10 ways and the 2nd spot in 9 ways.

Sorry, but I normally get confused with when to use Combinations and Permutations. Can you please clarify?
Show more

\(C^2_{10}\), which is 10*9/2 is the number of two entrees possible when the order of entrees does not matter.

\(P^2_{10}\), which is 10*9 is the number of two entrees possible when the order of entrees matters, i.e. when we differentiate between (entree X, entrees Y) from (entree Y, entrees X).
General Discussion
User avatar
Patronus
User avatar
Joined: 21 Aug 2014
Last visit: 10 Nov 2016
Posts: 101
Own Kudos:
1,005
 [4]
Given Kudos: 49
Schools: Tepper '18 (WL) Krannert '18 (A) Kelley '18 (M) Simon '18 (WA) Fisher '18 (WD)
GMAT 1: 610 Q49 V25
GMAT 2: 730 Q50 V40
Schools: Tepper '18 (WL) Krannert '18 (A) Kelley '18 (M) Simon '18 (WA) Fisher '18 (WD)
GMAT 2: 730 Q50 V40
Posts: 101
Kudos: 1,005
 [4]
A restaurant serves 6 varieties of appetizers, 10 different entrees an 24 Jun 2015, 10:57
4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Patronus
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)


1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\);
1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\).

Total = A.

Answer: A.
Show more
Thank you for the short answer Bunuel.

Can you please tell me why we should use \(\frac{(10*9)}{2}\) and not 10*9?
I solved it by thinking we have to fill 2 spots out of 10 contenders (entrees). Therefore, first spot can be filled in 10 ways and the 2nd spot in 9 ways.

Sorry, but I normally get confused with when to use Combinations and Permutations. Can you please clarify?
User avatar
Mo2men
User avatar
Joined: 26 Mar 2013
Last visit: 09 May 2023
Posts: 2,426
Own Kudos:
1,508
Given Kudos: 641
Concentration: Operations, Strategy
Schools: Erasmus (II)
Products:
My Reviews
Schools: Erasmus (II)
Posts: 2,426
Kudos: 1,508
A restaurant serves 6 varieties of appetizers, 10 different entrees an 25 Jun 2015, 01:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Patronus
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)


1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\);
1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\).


Answer: A.
Show more

Hi Bunnel,

Why is there (+) in choice A? what does it mean? what not multiplication sign (*)?

Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 24 Apr 2026
Posts: 109,814
Own Kudos:
811,028
 [1]
Given Kudos: 105,871
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: 109,814
Kudos: 811,028
 [1]
A restaurant serves 6 varieties of appetizers, 10 different entrees an 25 Jun 2015, 02:15
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Mo2men
Bunuel
Patronus
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)


1 appetizer out of 6, 1 entrees out of 10, 1 dessert out of 4: \(6*10*4\);
1 appetizer out of 6, 2 entrees out of 10, 1 dessert out of 4: \(6*C^2_{10}*4=6*\frac{(10*9)}{2} * 4\).


Answer: A.

Hi Bunnel,

Why is there (+) in choice A? what does it mean? what not multiplication sign (*)?

Thanks
Show more

Principle of Multiplication
If an operation can be performed in ‘m’ ways and when it has been performed in any of these ways, a second operation that can be performed in ‘n’ ways then these two operations can be performed one after the other in ‘m*n’ ways.

Principle of Addition
If an operation can be performed in ‘m’ different ways and another operation in ‘n’ different ways then either of these two operations can be performed in ‘m+n’ ways (provided only one has to be done).
User avatar
Nunuboy1994
User avatar
Joined: 12 Nov 2016
Last visit: 24 Apr 2019
Posts: 554
Own Kudos:
126
Given Kudos: 167
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
Posts: 554
Kudos: 126
A restaurant serves 6 varieties of appetizers, 10 different entrees an 02 Sep 2017, 14:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Patronus
A restaurant serves 6 varieties of appetizers, 10 different entrees and 4 different desserts. In how many ways can one make a meal if one chooses an appetizer, at least one and at most two different entrees and one dessert?

A) \((6*10*4) + (6*\frac{(10*9)}{2} * 4)\)
B) 6*10*4
C) 6*10*2*4
D) 6*9*4
E) \(\frac{6*10*4}{2}\)
Show more

There's two basic scenarios

6c1 x 10c1 x 4c1 = [6 x 10 x 4]

6c1 x 10c2 x 4c1 = [6 x 45 x 4]

Account for both possibilities hence
How many possibilities with 10c1 + how many possibilities with 10c2
[6 x 10 x 4] + [6 x 45 x 4]

A
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
A restaurant serves 6 varieties of appetizers, 10 different entrees an 26 Dec 2025, 08:01
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
109814 posts
Krunaal
Tuck School Moderator
853 posts