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.

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

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.

The number of ways to select the photographs is:

5C3 + 5C4

(5 x 4 x 3)/(3 x 2) + 5

10 + 5 = 15

Answer: D