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A certain restaurant offers 6 kinds of cheese and 2 kinds of

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A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink] New post 21 Dec 2009, 11:09
00:00
A
B
C
D
E

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  25% (medium)

Question Stats:

65% (01:45) correct 35% (00:42) wrong based on 66 sessions
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

A) 8
B) 12
C) 15
D) 21
E) 27
[Reveal] Spoiler: OA

Last edited by walker on 05 Apr 2012, 19:35, edited 2 times in total.
Edited the question and added the OA
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Re: combinations [#permalink] New post 21 Dec 2009, 11:35
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chetan2u wrote:
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

A) 8
B) 12
C) 15
D) 21
E) 27


As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:

A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15

B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12

A+B=15+12=27

Answer: E.
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Re: combinations [#permalink] New post 21 Dec 2009, 12:02
Yup same approach Got E as well.
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Re: combinations [#permalink] New post 22 Dec 2009, 10:25
Please add this one to our combinatorics collection questions.

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Re: Math - Problem [#permalink] New post 26 Jan 2010, 12:04
ahirjoy wrote:
Hi All,

Need your help in solving the below problem,

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruits for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different desert platters could the restaurant offer?

A:- 8/12/15/21/27


1 of each: 1 fruit * 1 cheese = 2 * 6 = 12 possibilities
2 of each: Well, you only have 2 fruits, so only one choice here. With 6 cheese, and 2 places, where order does not matter, you get 6!(6-2)!2! = 6!/4!2 = 6*5/2 = 15

So 15 + 12 = 27 total possible platters...
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Re: combinations [#permalink] New post 17 Oct 2010, 18:17
E.
In case we serve 1 of each 6C1*2C1=6*2=12
In case we serve 2 of each 6C2*2C2=15*1=15
=> 15+12=27

.
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Re: combinations [#permalink] New post 18 Jul 2011, 23:54
Bunuel wrote:
chetan2u wrote:
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

A) 8
B) 12
C) 15
D) 21
E) 27


As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:

A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15

B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12

A+B=15+12=27

Answer: E.



How do we get 6c2 * 2c2?? Can someone break it down ? Do we read * as "AND" 2 cheese can be chosen from 6 cheese in 6c2 ways AND 2fruit can be choosen from 2 in 2c2 ways hence whenver we have AND we multiply???
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Re: Math - Problem [#permalink] New post 14 Oct 2011, 13:58
Answer:
Option E = 27.

Explanation:

For 1 item each of Fruit & Cheese : 2 x 6 = 12

For 2 item each: Both fruit go in the dish. And we have to select 2 cheese out of 6 i.e. 6-C-2 = 6!/(4! x 2!) = 15

Total Menu Items = 15 +12 = 27
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Re: Math - Problem [#permalink] New post 16 Oct 2011, 12:03
1) One of Each, Therefore 2*6

2) Two of Each,But we have two fruits anyway.So that`ll be one. Rest two Cheese variants can be chosen from the 6 types in 6 C 2 ways.
6! / (4! * 2!)

Total of 1 & 2 gives 27.
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Re: Math - Problem [#permalink] New post 19 Oct 2011, 03:29
ahirjoy wrote:
Hi All,

Need your help in solving the below problem,

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruits for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different desert platters could the restaurant offer?

A:- 8/12/15/21/27


6C1*2C1 + 6C2*2C2 = 27
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Re: Math - Problem [#permalink] New post 01 Nov 2011, 06:07
the platter could contain either 2 items or 4 items.
2-items: 6*2 = 12

4-items: \frac{6*5}{2!}*\frac{2*1}{2!} = 15

total = 15+12 = 27
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Re: Math - Problem [#permalink] New post 01 Nov 2011, 13:20
E

Two possibilities, either 2 types of each or 1 type of each.

For 2 types: 6C2 * 2C2 = 15 * 1 = 15
For 1 type: 6C1 * 2C1 = 6 * 2 = 12

Total is 15+12 = 27.
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Re: combinations [#permalink] New post 09 Feb 2012, 11:32
Expert's post
siddhans wrote:
Bunuel wrote:
chetan2u wrote:
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?

A) 8
B) 12
C) 15
D) 21
E) 27


As dessert platter should contain equal number of kinds of cheese and fruits, desert can contain:

A. 2 kinds of cheese and 2 kinds of fruits --> 6C2*2C2=15*1=15

B. 1 kind of cheese and 1 kind of fruit --> 6C1*2C1=6*2=12

A+B=15+12=27

Answer: E.


How do we get 6c2 * 2c2?? Can someone break it down ? Do we read * as "AND" 2 cheese can be chosen from 6 cheese in 6c2 ways AND 2fruit can be choosen from 2 in 2c2 ways hence whenver we have AND we multiply???


Yes, your understanding is correct.

It's called Principle of Multiplication: if one event can occur in m ways and a second can occur independently of the first in n ways, then the two events can occur in m*n ways.
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Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink] New post 10 Feb 2012, 09:08
6+6+6c2=27.
E is the answer .
The above expression denoted choosing one cheese type and one fruit type (6+6) ways ,for each type of fruit there are 6 types of cheese that can be selected .
And finally where there are two types of cheese and fruits respectively .
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Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink] New post 15 Feb 2012, 10:52
I got e as well

For 2 types: 6C2 * 2C2 = 15 * 1 = 15
For 1 type: 6C1 * 2C1 = 6 * 2 = 12

exact approach
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Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink] New post 15 Aug 2014, 23:54
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Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of   [#permalink] 15 Aug 2014, 23:54
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