Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
20 May 2010, 14:57
Kudos
Bookmarks
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
50% (00:57) correct
50%
(01:25)
wrong
based on 3
sessions
History
Date
Time
Result
Not Attempted Yet
G, M, P, J, B and C are supposed to sit in 6 different seats. But M and J won't sit together, how many different arrangements are possible?
OA:
OA:
480
So, I know I can calculate the possibilities w/o constraints and subtract the possibilities with constraints and get the answer as 6! - 5! to get 480. What I am trying to think is in terms of the following (which works for most problems, but I can't figure out why this model doesn't fit this situation)
I have 6 possibilities for Seat 1 and I assume its M, so possibilities = 6.
Now, I have 4 possibilities for Seat 2 because J won't sit with M, so possibilities = 4
Now, I have 4 possibilities again for Seat 3 because M is back in the group, so possibilities = 4
And then finally 3 and 2, so possibilities = 3 * 2
Multiplying, 6 * 4 * 4 * 6 = 576 possibilities.
Where am I formulating this wrongly?
Thanks in advance.
I have 6 possibilities for Seat 1 and I assume its M, so possibilities = 6.
Now, I have 4 possibilities for Seat 2 because J won't sit with M, so possibilities = 4
Now, I have 4 possibilities again for Seat 3 because M is back in the group, so possibilities = 4
And then finally 3 and 2, so possibilities = 3 * 2
Multiplying, 6 * 4 * 4 * 6 = 576 possibilities.
Where am I formulating this wrongly?
Thanks in advance.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
20 May 2010, 18:36
Kudos
Bookmarks
abc123def
To solve this you can do one of two things:
1. find the total number of outcomes and then subtract the number of invalid outcomes based on the constraints
2. Count the number of valid outcomes based on the constraints
1) total number of outcomes = 6!
invalid outcomes would be when M & J sit together can be visualized by the following:
M J _ _ _ _
_ M J _ _ _
_ _ M J _ _
_ _ _ M J _
_ _ _ _ M J
this equals 5*4! = 5!
but you need to consider that M J do not need to be in that order, it could be J M, so multiply your outcomes by 2. Therefore your total invalid outcomes based on the constrains is 2*5! = 240
and thus the answer is 6! - 2*5! = 720-240 = 480
(looks like you forgot the 2 multiplier in your answer)
2) the number of valid outcomes can be visualized as follows:
M _ J _ _ _
M _ _ J _ _
M _ _ _ J _
M _ _ _ _ J
_ M _ J _ _
_ M _ _ J _
_ M _ _ _ J
_ _ M _ J _
_ _ M _ _ J
_ _ _ M _ J
so we have (4+3+2+1)*4! = 10*4!
but we have to consider that M J do not to need to be in that order, it could be J M, so double what we got to get: 2*10*4! = 480
your logic in trying to this problem using approach #2 is off. Although you can use this method when doing permutations, the constraints don't allow you to do it this way because depending on who is in the first seat the values for the other seats will be different. Avoid using this when there are dependencies on position.
In your calculations, first you are saying that there is 6 possibilities for the first seat, but then you calculate for when that seat is for M, this would invalidate the first 6 because setting that seat to M as in your assumption would make the first value a 1.
whenever you see dependencies, keep it simple and avoid confusion, use the following principles:
1. find the total number of outcomes and then subtract the number of invalid outcomes based on the constraints
2. Count the number of valid outcomes based on the constraints
Hope that helps..
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
