Combination

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mgmt_gmat: Master | Next Rank: 500 Posts; Posts: 221; Joined: Mon Dec 22, 2008 6:24 pm; Thanked: 2 times

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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Source: Beat The GMAT — Problem Solving | Fri Feb 12, 2010 2:13 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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 Ã— 15 = [spoiler]90[/spoiler].

[spoiler]D[/spoiler]

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

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

Always borrow money from a pessimist, he doesn't expect to be paid back.

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Osirus@VeritasPrep: GMAT Instructor; Posts: 1578; Joined: Thu May 28, 2009 8:02 amFollowed by: 34 members; Thanked: 128 times; GMAT Score:760

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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Veritas Prep

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