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A certain restaurant offers 8 different salads

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by M7MBA » Fri Apr 20, 2018 2:22 am
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A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?

A. 120
B. 240
C. 480
D. 600
E. 1200

The OA is the option D.

Should I use combinations? Is not 8*5*6*5=1200?
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by Vincen » Fri Apr 20, 2018 2:57 am
Hello M7MBA.

You have to use combinations.

There are:

- 8 different salads and the customer choose ONE salad.
- 5 different main courses and the customer choose ONE main course.
- 6 different desserts and the customer choose TWO desserts.

The math that represents the information above is: $$8\ C\ 1\ \cdot\ 5\ C\ 1\ \cdot\ 6\ C\ 2\ =\ \frac{8!}{7!\cdot1!}\cdot\frac{5!}{4!1!}\cdot\frac{6!}{4!2!}=8\cdot5\cdot\frac{6\cdot5}{2}=40\cdot15=600.$$ Hence, the correct asnwer is the option D.
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by Brent@GMATPrepNow » Fri Apr 20, 2018 5:26 am
M7MBA wrote:A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?

A. 120
B. 240
C. 480
D. 600
E. 1200
Take the task of creating a meal and break it into stages.

Stage 1: Select 1 salad
There are 8 different salads from which to choose, so we can complete stage 1 in 8 ways

Stage 2: Select 1 main course
There are 5 different main courses from which to choose, so we can complete stage 2 in 5 ways

Stage 3: Select 2 different desserts
Since the order in which we select the desserts does not matter, we can use combinations.
We can select 2 desserts from 6 desserts in 6C2 ways (15 ways)
So, we can complete stage 3 in 15 ways

ASIDE: If anyone is interested, we have a free video on calculating combinations (like 11C2) in your head: https://www.gmatprepnow.com/module/gmat ... /video/775

You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat ... /video/776

Then you can try solving the following questions:

EASY
- https://www.beatthegmat.com/what-should- ... 67256.html
- https://www.beatthegmat.com/counting-pro ... 44302.html
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- https://www.beatthegmat.com/permutation- ... 57412.html
- https://www.beatthegmat.com/simple-one-t270061.html


MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
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DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
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- https://www.beatthegmat.com/permutation-t122873.html
- https://www.beatthegmat.com/no-two-ladie ... 75661.html
- https://www.beatthegmat.com/combinations-t123249.html


Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Sat Apr 21, 2018 8:41 am
Salad can be chosen in 8C1 ways.

Main Course can be chosen in 5C1 ways.

Desserts can be chosen in 6C2 ways.

Therefore the answer will be the product which is as follows,

8C1*5C1*6C2=8*5*15=600

Hence Answer D.

Regards!
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by Jeff@TargetTestPrep » Mon Apr 23, 2018 4:50 pm
M7MBA wrote:A certain restaurant offers 8 different salads, 5 different main courses, 6 different desserts. If customers choose one salad, one main course and two different desserts for their meal, how many different meals are possible?

A. 120
B. 240
C. 480
D. 600
E. 1200
The number of meals is:

8C1 x 5C1 x 6C2 = 8 x 5 x (6 x 5)/2! = 8 x 5 x 15 = 600

Answer: D

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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