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A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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27 Sep 2009, 18:38

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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 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

Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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26 Jan 2010, 13:04

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...
_________________

________________________________________________________________________ Andrew http://www.RenoRaters.com

Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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19 Jul 2011, 00:54

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???

Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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19 Oct 2011, 04:29

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
_________________

GMAT is an addiction and I am darn addicted

Preparation for final battel: GMAT PREP-1 750 Q50 V41 - Oct 16 2011 GMAT PREP-2 710 Q50 V36 - Oct 22 2011 ==> Scored 50 in Quant second time in a row MGMAT---- -1 560 Q28 V39 - Oct 29 2011 ==> Left Quant half done and continued with Verbal. Happy to see Q39

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.
_________________

Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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10 Feb 2012, 10:08

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 .
_________________

Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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16 Aug 2014, 00:54

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Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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26 May 2015, 23:24

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This question is a good example where both OR and AND events are used. Let's see how such events are treated when finding the number of ways of an event happening.

Given Info We are given that a restaurant in its dessert platter offers 6 kinds of cheese and 2 kinds of fruits. We are asked to find the number of ways a dessert platter can be offered if the platter contains equal kinds of fruits and cheese.

Approach We observe here that there are lesser kinds of fruits than the cheese. Hence the number of ways the platter can be offered is limited by the number of fruits.

Since a platter would be incomplete without any of the fruit or cheese, for the event to occur( i.e. platter to be served) a platter should have fruit AND cheese.

Also, there can be a case where a platter may have 1 fruit AND 1 cheese OR 2 fruits AND 2 cheese. Hence, the event(i.e. platter to be served) can occur in either of the ways.

Number of ways the platter can be served = Number of ways of picking up 1 fruit out of 2 fruits AND number of ways of picking up 1 cheese out of 6 cheese OR Number of ways of picking up 2 fruits out of 2 fruits AND number of ways of picking up 2 cheese out of 6 cheese

Working Out Number of ways in which 1 fruit can be picked out of 2 fruits = \(2_{c_{1}}\)

Number of ways in which 1 cheese can be picked out of 6 cheese = \(6_{c_{1}}\)

Hence number of ways in which a platter having 1 fruit and 1 cheese can be served = \(2_{c_{1}}\) \(*\) \(6_{c_{1}}\) \(= 2 * 6 = 12\)

Similarly, Number of ways in which 2 fruits can be picked out of 2 fruits = \(2_{c_{2}}\)

Number of ways in which 2 cheese can be picked out of 6 cheese = \(6_{c_{2}}\)

Hence number of ways in which a platter having 2 fruits and 2 cheese can be served = \(2_{c_{2}}\) \(*\) \(6_{c_{2}}\) \(= 1 * 15 = 15\)

Therefore total number of ways of serving a dessert platter \(= 12 + 15 = 27\)

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

Since the plates have to contain an equal number of cheese and fruit types, the only possibilities are 1 kind of cheese and 1 kind of fruit or 2 types of cheese and 2 types of fruit.

Case 1: Cheese: n=6, r = 1 (6x5x4x3x2x1) 1(5x4x3x2x1)

Fruit: n=2, r=1 (2x1) 1(1)

Combining cheese and fruit 6 x 2 = 12

Case 2: Cheese n = 6, r = 2 (6x5x4x3x2x1) 2x1 (4x3x2x1) =15

Fruit: There are only two fruits, so there is only one combination.

Re: A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]

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30 May 2016, 21:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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