Maude wrote:

Hello

Please need help to understand the following

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!.

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:

PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.

What are GMAT Club Tests?

25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership