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Combination

by mgmt_gmat » Fri Feb 12, 2010 2:13 am
The buyer of a new home must choose 2 of 4 types of flooring and 2 of 6 paint colors. How many different combinations of type of flooring and paint color are available to the home buyer?
A. 4
B. 24
C. 48
D. 90
E. 96
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by sanju09 » Fri Feb 12, 2010 2:59 am
mgmt_gmat wrote:The buyer of a new home must choose 2 of 4 types of flooring and 2 of 6 paint colors. How many different combinations of type of flooring and paint color are available to the home buyer?
A. 4
B. 24
C. 48
D. 90
E. 96
The different combinations of type of flooring that are available to the home buyer is 4C2 = 6 and the different combinations of type of paint color that are available to the home buyer is 6C2 = 15, and hence the different combinations of type of flooring and paint color that are available to the home buyer = 6 × 15 = [spoiler]90[/spoiler].

[spoiler]D[/spoiler]
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by ajith » Fri Feb 12, 2010 11:40 am
mgmt_gmat wrote:The buyer of a new home must choose 2 of 4 types of flooring and 2 of 6 paint colors. How many different combinations of type of flooring and paint color are available to the home buyer?
A. 4
B. 24
C. 48
D. 90
E. 96
No of ways in which he can choose 2 of 4 types of flooring = 4C2 = 6 ways
No of ways in which he can choose 2 of 6 paint colors = 6C2 = 15 ways

Total no of ways = 6*15 = 90 ways
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by Osirus@VeritasPrep » Fri Feb 12, 2010 11:46 am
An easier way to do this is to use the Manhattan GMAT anagram method

total number of ways to floring

A B C D
Y Y N N

4!/(2! * 2!) = 6

total number of ways to choose paint colors

A B C D E F
Y Y N N N N

6!/(4! * 2!) = 15

15* 6 = 90
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