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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Carly has 3 movies that she can watch during the weekend: 1 Action movie, 1 Comedy, and 1 Drama. However, she needs to watch the Drama 3 times. Assuming Carly has time for 5 movies and intends to watch all of them, in how many ways can she do so?

Below is a revised version of this question:

Carly has three movies that she can watch during the weekend: an action movie, a comedy, or a drama. However, she wants to watch the same drama movie three times, an action movie once and a comedy movie also once. In how many different ways can she arrange these five screenings?

A. 6 B. 20 C. 24 D. 60 E. 120

The number of different ways Carly can watch Drama, Drama, Drama, Action, Comedy (DDDAC) is basically the number of arrangements of 5 letters DDDAC out of which 3 D's are identical, so it's \(\frac{5!}{3!}=20\).

Answer: B.

This is the way the question should be phrased to avoid ambiguity.

Otherwise the original question can also lead to the following solution: (3D1C1A )5!/3!+ (3D2C+3D2A)2*5!/3!2! +(4D1A+4D1C)2*5!/4! +(5D)5!/5! = 46 _________________

That's so cool! I always had difficulty in solving this type of question. After going thru the book veritas prep combinatorics and probability I feel huuuuge progress and easily solve these questions!!!

The duplication effect occurs here; all three viewings of the Drama movie are equal - not independent of each other. Moreover, it's not logical to think that the first viewing of drama can go after the third viewing of the drama, and the third viewing of the drama to come before the first.

This is my plan: in total there are 5 slots for all movies For the 2 movies that watched only one time: the first movie: there are 5 slots the 2nd movie: there are 4 slots (5 minus one picked for the first movie) after selecting slots for 2 movies, there are to slot for the drama and any order are the same ---> 1 way

five things can be arranged in 5!ways. = 120 3 of them are similar , hence 5!/3! = 20 ways

P.S. - In case the three drama movies had been different , I mean, she had the choice to watch D1, D2 and D3 then the arrangements would have been 5!=120 only. But since the drama movie is the same D,D,D, HENCE 5!/3!