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.
To apply for the position of photographer at a local...
This topic has expert replies
GMAT/MBA Expert
- ErikaPrepScholar
- Legendary Member
- Posts: 503
- Joined: Thu Jul 20, 2017 9:03 am
- Thanked: 86 times
- Followed by:15 members
- GMAT Score:770
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.
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/
Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/
Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial
Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog
GMAT/MBA Expert
- 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
Since the order in which we select the pictures does not matter, we can use combinations.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
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
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7242
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
The number of ways to select the photographs is: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.
5C3 + 5C4
(5 x 4 x 3)/(3 x 2) + 5
10 + 5 = 15
Answer: D
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews