In how many ways can 3 different portraits be mounted

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Sat Apr 07, 2018 12:54 am

In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

The OA is the option E .

It shouldn't be 9? 3 walls and 3 portraits, 3*3=9. No? I need some help here. Thanks in advanced.

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Apr 07, 2018 1:33 am

M7MBA wrote:In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

The OA is the option E .

It shouldn't be 9? 3 walls and 3 portraits, 3*3=9. No? I need some help here. Thanks in advanced.

Hello M7MBA.

Let's see, we have:

- 4 walls from which we have to pick 3, it can be done as follows $$4C3\ =\frac{4!}{3!1!}=4\ different\ ways.$$

- We need to arrange 3 portraits, this can be done in 3! different ways, that is to say, 6 different ways.

Therefore, the number of ways that 3 different portraits can be mounted on 3 of the four walls inside a room is given by $$4\cdot3!=4\cdot6=24\ different\ ways.$$ This implies that the correct answer is the option E .

I hope it can help you.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Apr 07, 2018 2:15 am

M7MBA wrote:In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Number of options for the first portrait = 4. (Any of the 4 walls.)
Number of options for the second portrait = 3. (Any of the 3 remaining walls.)
Number of options for the last portrait = 2. (Either of the 2 remaining walls.)
To combine the options above, we multiply:
4*3*2 = 24.

The correct answer is E.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8136; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu Jul 05, 2018 3:53 pm

M7MBA wrote:In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

Solution:

We have 4C3 = 4 ways to choose the 3 of the 4 walls. Next we have 3! = 6 ways to put the portraits onto the 3 walls we've chosen. Thus, there are 4 x 6 = 24 ways to mount these portraits.

Answer: E

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