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:

6 persons are going to theater and will sit next to each oth [#permalink]

Show Tags

16 Jun 2010, 20:08

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

75% (03:07) correct
25% (00:04) wrong based on 8 sessions

HideShow timer Statistics

6 persons are going to theater and will sit next to each other in 6 adjacent seats. But Martia and Jan can not sit next to each other. In how many arrangement can this be done

I understood that the restriction must be deal first by finding the number of way the restriction happen and remove from the total number of way to arrange the n !

It is 2 ! for arrangement and 4 ! for the remaining 4 people

but what I don t understand is why it is time by 5 as the OA gives

I saw some other type like that

For instance digit 1,2,3,4,5 IF EACH DIGIT is used only once how many ways can each digit be arranged such 2 and 4 are not adjacent - In this case the restriction is 2!x4! not multiplied by anything else Can anyone explain me why

Assuming the two sit next to each other, we have 5!x2 arrangements (This is because when they are sitting next to each other, we can consider both of them as one "unit" and hence there are 5 units, i.e them and the other 4 people. This will lead to an arrangement of 5! and then between them, they can be seated in two ways, so it's 2x5!)

So answer = Total - Arrangements with them sitting next to each other

= 6! - 2x5! = 5! x 4 = 480

I think you assumed they were sitting next to each other and did only the 2! and 4!

What are the numbers given in the official answer? I believe you only mentioned word choices.

6 persons are going to theater and will sit next to each other in 6 adjacent seats But Martia and Jan can not sit next to each other .In how many Arrangement can this be done

I understood that the restriction must be deal first by finding the number of way the restriction happen and remove from the total number of way to arrange the n !

It is 2 ! for arrangement and 4 ! for the remaining 4 people

but what I don t understand is why it is time by 5 as the OA gives

I saw some other type like that

For instance digit 1,2,3,4,5 IF EACH DIGIT is used only once how many ways can each digit be arranged such 2 and 4 are not adjacent - In this case the restriction is 2!x4! not multiplied by anything else Can anyone explain me why

thanks for your Time

regards

Hi, and welcome to Gmat Club! Below is the solution for your problem.

You are right saying that probably the best way to deal with the questions like this is to count total # of arrangements and then subtract # of arrangements for which opposite of restriction occur. But the way you are calculating the later is not correct.

Total # of arrangements of 6 people (let's say A, B, C, D, E, F) is \(6!\). # of arrangement for which 2 particular persons (let's say A and B) are adjacent can be calculated as follows: consider these two persons as one unit like {AB}. We would have total 5 units: {AB}{C}{D}{E}{F} - # of arrangement of them 5!, # of arrangements of A and B within their unit is 2!, hence total # of arrangement when A and B are adjacent is \(5!*2!\).

# of arrangement when A and B are not adjacent is \(6!-5!*2!\).

In your example about 5 digits the answer would be: Total # of arrangements of 5 distinct digits is \(5!\). # of arrangement for which 2 digits 2 and 4 are adjacent is: consider these two digits as one unit like {24}. We would have total 4 units: {24}{1}{3}{5} - # of arrangement of them 4!, # of arrangements of 2 and 4 within their unit is 2!, hence total # of arrangement when 2 and 4 are adjacent is \(4!*2!\).

# of arrangement when 2 and 4 are not adjacent is \(5!-4!*2!\).

Re: 6 persons are going to theater and will sit next to each oth [#permalink]

Show Tags

18 Dec 2015, 12:57

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: 6 persons are going to theater and will sit next to each oth [#permalink]

Show Tags

22 Dec 2015, 02:12

Expert's post

Maude wrote:

6 persons are going to theater and will sit next to each other in 6 adjacent seats. But Martia and Jan can not sit next to each other. In how many arrangement can this be done

6 person can sit on 6 seats in way = 6*5*4*3*21 = 6! = 720

6 person can sit on 6 seats in ways such that Martia and Jan sit next to each other = (5*4*3*2*1)*(2!) = 5!*2! = 240

READ:http://gmatclub.com/forum/620-to-760-getting-reborn-161230.html Classroom Centre Address: GMATinsight 107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075 ______________________________________________________ Please press the if you appreciate this post !!

Re: 6 persons are going to theater and will sit next to each oth [#permalink]

Show Tags

22 Dec 2015, 03:40

the quick formular for this kind of questions is solve removing the constraint - the opposite of the constraint. Hence, 6! - 5! the opposite of the constraint is if the two guys must sit next to each other, that is, they are one, hence you have 5. how many ways can you arrange 6 unique letters minus how many ways can you arrange 5 unique letters

Re: 6 persons are going to theater and will sit next to each oth [#permalink]

Show Tags

22 Dec 2015, 04:06

Expert's post

Nez wrote:

the quick formular for this kind of questions is solve removing the constraint - the opposite of the constraint. Hence, 6! - 5! the opposite of the constraint is if the two guys must sit next to each other, that is, they are one, hence you have 5. how many ways can you arrange 6 unique letters minus how many ways can you arrange 5 unique letters

Hi, you have found the correct method but missed out the final step.. both are taken as one and we get the arrangement as 5! but within the two both can be arranged in 2! ways.. so answer becomes 6!-5!*2 _________________

MBA Admission Calculator Officially Launched After 2 years of effort and over 1,000 hours of work, I have finally launched my MBA Admission Calculator . The calculator uses the...

Final decisions are in: Berkeley: Denied with interview Tepper: Waitlisted with interview Rotman: Admitted with scholarship (withdrawn) Random French School: Admitted to MSc in Management with scholarship (...

The London Business School Admits Weekend officially kicked off on Saturday morning with registrations and breakfast. We received a carry bag, name tags, schedules and an MBA2018 tee at...