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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

To apply for the position of photographer at a local...

by AAPL » Tue Nov 14, 2017 6:57 pm

To apply for the position of photographer at a local magazine, Veronica needs to include three or four of her pictures in an envelope accompanying her application. If she has pre-selected five photos representative of her work, how many choices does she has to provide the photos for the magazine?

(A) 5
(B) 10
(C) 12
(D) 15
(E) 50

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Nov 14, 2017 6:57 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 am; Thanked: 86 times; Followed by:15 members; GMAT Score:770

by ErikaPrepScholar » Wed Nov 15, 2017 7:07 am

We have two possible combinations here - Veronica can choose 3 photos out of her 5 or 4 photos out of her 5.

5 choose 3:
$$\frac{5!}{2!3!}=\frac{5\cdot4}{2\cdot1}=10$$

5 choose 4:
$$\frac{5!}{1!4!}=\frac{5}{1}=5$$

So Veronica can choose 3 photos in 15 ways and choose 4 photos in 4 ways. Since Veronica can submit either 3 or 4 photos, we add these choices together to get 15 total choices.

Note: we use the combination formula here because order does not matter - she can put the same 3 or 4 photos in the envelope in any order and it is still the same submission.

Erika John - Content Manager/Lead Instructor
https://gmat.prepscholar.com/gmat/s/

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

To apply for the position of photographer at a local...

by Brent@GMATPrepNow » Wed Nov 15, 2017 11:24 am

AAPL wrote:To apply for the position of photographer at a local magazine, Veronica needs to include three or four of her pictures in an envelope accompanying her application. If she has pre-selected five photos representative of her work, how many choices does she has to provide the photos for the magazine?

(A) 5
(B) 10
(C) 12
(D) 15
(E) 50

Since the order in which we select the pictures does not matter, we can use combinations.

We must consider two possible cases:
1) Veronica includes 3 of her pictures
We can select 3 pictures from 5 pictures in 5C3 ways
5C3 = 10

2) Veronica includes 4 of her pictures
We can select 4 pictures from 5 pictures in 5C4 ways
5C4 = 5

ASIDE: Here's a video that shows you how to quickly calculate combinations (like 5C3) in your head: https://www.gmatprepnow.com/module/gmat- ... /video/789

Total number of possibilities = 10 + 5
= 15
= D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Oct 16, 2019 6:11 pm

AAPL wrote:To apply for the position of photographer at a local magazine, Veronica needs to include three or four of her pictures in an envelope accompanying her application. If she has pre-selected five photos representative of her work, how many choices does she has to provide the photos for the magazine?

(A) 5
(B) 10
(C) 12
(D) 15
(E) 50

The OA is D.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.