Standing in the line

Expert replies

JeetGulia: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 14, 2010 4:46 am; Thanked: 3 times

by JeetGulia » Thu Jul 29, 2010 1:55 pm

In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Frederick, Gale, and Harold?

a) 1,008
b) 1,296
c) 1,512
d) 2,016
e) 2,268

Like this post

Source: Beat The GMAT — Problem Solving | Thu Jul 29, 2010 1:55 pm

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Thu Jul 29, 2010 7:45 pm

Solution:
Let people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be A, B, C, D, E, F, G and H respectively.

Now A, B and C must be before F,G and H.
Two cases can arise.
Either (1) D and E are together
or
(2) D and E are not together.
Consider (1) first.
So if A B C F G H are arranged like this and D and E have to be together, there are 7 places in which they can be put in 7P1 *2 or 14 ways.
Also A. B and C can be arranged among themselves in 3! or 6 ways and F, G and H can be arranged among themselves in 3! or 6 ways.
Or If D and E have to be together, they can be arranged in 14*6*6 = 504 ways.
Consider (2) then.
If they are arranged like this A B C F G H, there are 7 places between them where D and E can be placed.
This can be done in 7P2 or 7*6 = 42 ways.
Also A. B and C can be arranged among themselves in 3! or 6 ways and F, G and H can be arranged among themselves in 3! or 6 ways.
So the possible arrangements we can have is 42*6*6 = 1,512.

Or total number of arrangements is 1512+504 = 2016 ways.

The correct answer is (D).

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

Like this post

JeetGulia: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 14, 2010 4:46 am; Thanked: 3 times

by JeetGulia » Fri Jul 30, 2010 2:02 am

Rahul@gurome wrote:Solution:
Let people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be A, B, C, D, E, F, G and H respectively.

Now A, B and C must be before F,G and H.
Two cases can arise.
Either (1) D and E are together
or
(2) D and E are not together.
Consider (1) first.
So if A B C F G H are arranged like this and D and E have to be together, there are 7 places in which they can be put in 7P1 *2 or 14 ways.
Also A. B and C can be arranged among themselves in 3! or 6 ways and F, G and H can be arranged among themselves in 3! or 6 ways.
Or If D and E have to be together, they can be arranged in 14*6*6 = 504 ways.
Consider (2) then.
If they are arranged like this A B C F G H, there are 7 places between them where D and E can be placed.
This can be done in 7P2 or 7*6 = 42 ways.
Also A. B and C can be arranged among themselves in 3! or 6 ways and F, G and H can be arranged among themselves in 3! or 6 ways.
So the possible arrangements we can have is 42*6*6 = 1,512.

Or total number of arrangements is 1512+504 = 2016 ways.

The correct answer is (D).

Rahul..Could you please explain little bit how did you come up with

if A B C F G H are arranged like this and D and E have to be together, there are 7 places in which they can be put in 7P1 *2 or 14 ways.

and

If they are arranged like this A B C F G H, there are 7 places between them where D and E can be placed.
This can be done in 7P2 or 7*6 = 42 ways.

Like this post

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Fri Jul 30, 2010 2:59 am

Take the case when D and E are together. This means the cases where they are standing next to each other.
The possibilities are
D E A B C F G H or E D A B C F G H
A D E B C F G H or A E D B C F G H
A B D E C F G H or A B E D C F G H
.
.
.
.
A B C F G H D E or A B C F G H E D

As seen from above we get 7 places for DE, 5 between A, B, C, F, G and H,1 before A and 1 after H. 7P1 is taken because D E are taken as one item and they have to be arranged in any of the seven places. This is multiplied by 2 because for every D E there is a possibility of E D.

In the second case where D and E are not together, we get 7 places again and in these 7 places D and E can be arranged in 7P2 ways. Since they are not standing together they are taken as 2 items.

I hope it is clearer now!

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review