It is currently 21 Apr 2019, 08:37
My Tests

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

A film production company must submit 5 of its movies releas

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Founder
Founder
User avatar
Joined: 18 Apr 2015
Posts: 6200
Followers: 99

Kudos [?]: 1199 [0], given: 5712

CAT Tests
A film production company must submit 5 of its movies releas [#permalink] New post 09 Apr 2019, 02:03
Expert's post
00:00

Question Stats:

50% (00:00) correct 50% (02:09) wrong based on 2 sessions
A film production company must submit 5 of its movies released this year for consideration for an awards ceremony. This year, the company released 14 movies; 8 of these were horror movies and 6 were romantic comedies. If it submits at least 3 romantic comedies, how many groups of 5 movies can be submitted?

A. 276

B. 432

C. 560

D. 681

E. 686
[Reveal] Spoiler: OA

_________________

Get the 2 FREE GREPrepclub Tests

Manager
Manager
Joined: 04 Feb 2019
Posts: 204
Followers: 4

Kudos [?]: 85 [0], given: 0

CAT Tests
Re: A film production company must submit 5 of its movies releas [#permalink] New post 13 Apr 2019, 05:59
Expert's post
We have three different options here, and it's going to be easiest to just count them individually. We can have 3 romantic comedies and 2 horror movies, 4 romantic comedies and 1 horror movie, or all romantic comedies.

To start, let's count the ways we can choose 3 romantic comedies. There are 6 options for the first comedy, 5 for the second, and 4 for the third. That's a total of 6*5*4 = 120 different possibilities.

However, the order doesn't matter. Submitting movies A, B, and C is the same as submitting movies B, C, and A. So we need to divide out those repetitions. Each group of 3 can be arranged in 3! = 6 different ways, so we divide by 6 to get a total of \(\frac{120}{6} = 20\) different combinations of 3 romantic comedies to submit.

Now we have to pick 2 horror movies out of the list of 8. Following the same logic as before, we have 8 choices for the first movie, and 7 for the second, for a total of 8*7 = 56 possible pairs. However, each pair is counted twice. So we really only have 28 pairs.

Each of those 28 pairs of horror movies can be matched with any of the 20 groups of 3 comedies. So there are 28*20 = 560 options here in all.

Second, we could have 4 comedies and 1 horror movie. The calculation for the comedies will be \(\frac{6*5*4*3}{4*3*2*1} = 15\). There are 8 horror movies, which means we have 8 ways of picking 1 of them ;)

Put those together for 15*8 = 120 different ways of choosing 4 comedies and 1 horror movie.

Next, if we choose all 5 romantic comedies, then we're only leaving one comedy behind. There are 6 ways to choose that one to be left behind, and so 6 ways of choosing 5 romantic comedies.

Add up all our possibilities, and we get 560 + 120 + 6 = 686 possibilities in all.
Re: A film production company must submit 5 of its movies releas   [#permalink] 13 Apr 2019, 05:59
Display posts from previous: Sort by

A film production company must submit 5 of its movies releas

  Question banks Downloads My Bookmarks Reviews Important topics  


GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

Powered by phpBB © phpBB Group

Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.