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A certain restaurant offers 8 different salads, 5 different main cours

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A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 26 Feb 2015, 06:38
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A
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C
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E

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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

Kudos for a correct solution.

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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 26 Feb 2015, 08:50
In order to select x things from group of n things can be written as nCx

8C1*5C1*6C2= 8*5*15=600 answer is D
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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 26 Feb 2015, 09:18
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8c1 * 5c1 * 6c2 = 8*5*15 = 600

Answer D
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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 28 Feb 2015, 04:52
Bunuel 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

Kudos for a correct solution.


One salad can be chosen in 8C1 = 8 ways
One main course can be chosen in 5C1 = 5 ways
Two desserts can be chosen in 6C2 = 15 ways

Total number of ways = 8*5*15 = 600
Hence option D.

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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 02 Mar 2015, 06:18
Bunuel 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

Kudos for a correct solution.


MAGOOSH OFFICIAL SOLUTION:

To count the number of meals, we have to count the possibilities for the three components, and then, according to the Fundamental Counting Principle, we multiply. For more on the FCP, see this blog.

For salads, there are 8 possibilities. Done.

For main courses, there are 5 different possibilities. Done.

For desserts, there are 6 choices, but we pick two different choices. This would be 6C2. To calculate this, we can use the shortcut, nC2 = (n*(n-1))/2.

6C2 = (6*5)/2 = 15

So, there are 15 combinations of two different desserts.

For the number of meals, we multiply 8*5*15. We know 8*5 = 40. Then, we need 40*15. Well, 4*15 = 60, so 40*15 must be 600.

Answer = (D)
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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 25 Mar 2016, 13:17
Salad can be choosen in 8C1 ways
Main Course can be choosen in 5C1 ways
Desserts can be choosen in 6C2 ways
Therefore answer will be product which is as follows
8C1*5C1*6C2=8*5*15=600

Hence Answer-D
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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 20 Apr 2018, 06:31
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Bunuel 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

Kudos for a correct solution.


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

By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a meal) in (8)(5)(15) ways (= 600 ways)

Answer: D

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: A certain restaurant offers 8 different salads, 5 different main cours  [#permalink]

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New post 23 Apr 2018, 17:41
Bunuel 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
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Re: A certain restaurant offers 8 different salads, 5 different main cours   [#permalink] 23 Apr 2018, 17:41
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