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A certain restaurant offers 6 kinds of cheese and 2 kinds of [#permalink]
21 Dec 2009, 11:09

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

68% (01:37) correct
31% (00:52) wrong based on 38 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 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: Math - Problem [#permalink]
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...
_________________

________________________________________________________________________ Andrew http://www.RenoRaters.com

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: Math - Problem [#permalink]
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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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]
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 .
_________________