Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Feb 2009
Posts: 47
Schools: INSEAD,Nanyang Business school, CBS,

In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
05 Feb 2010, 13:18
1
This post received KUDOS
2
This post was BOOKMARKED
Question Stats:
57% (00:42) correct 43% (00:52) wrong based on 160 sessions
HideShow timer Statistics
In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other? (A) 112 (B) 96 (C) 84 (D) 72 (E) 60
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Working without expecting fruit helps in mastering the art of doing faultfree action !



CEO
Joined: 17 Nov 2007
Posts: 3486
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
05 Feb 2010, 13:31
1. the total number of permutations: 5! = 120 2. Let's consider Maggie and Lisa as one object, then the total number of permutations with Maggie and Lisa together: 4! = 24. 3. Take into account that [Maggie, Lisa] and [Lisa, Maggie] are different. 4. Maggie and Lisa cannot stand next to each other in: 120  2*24 = 72 ways.
_________________
HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android)  The OFFICIAL GMAT CLUB PREP APP, a musthave app especially if you aim at 700+  PrepGame



Intern
Joined: 19 Feb 2009
Posts: 47
Schools: INSEAD,Nanyang Business school, CBS,

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
05 Feb 2010, 13:52
Got it walker.. Thanks V.Much for this explanation
_________________
Working without expecting fruit helps in mastering the art of doing faultfree action !



Intern
Joined: 05 Nov 2014
Posts: 41
Concentration: Marketing, International Business

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
27 Jul 2015, 00:09
can we solve this with \(P^n_r\) formula?
_________________
Kudos = Thanks
"Yeah, you can get a nickel for boosting Starfall, but jacking Heal's a tenday stint in county. Now lifting Faerie Fire, they just let you go for that — it's not even worth the paperwork. But Reincarnation, man! That'll get you life!"



SVP
Joined: 08 Jul 2010
Posts: 2099
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
27 Jul 2015, 01:19
Subanta wrote: can we solve this with \(P^n_r\) formula? Jut a personal Suggestion: It's best to see the steps and work in steps in P&C problems rather than being dependent on formulasHowever, Answer to your query is as follows Quote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 5 girls can stand in line in \(P^5_5 = 120 ways\) 5 girls can stand in line in such that Maggie and Lisa stand together in \(P^4_4 * P^2_2= 48 ways\) Total favourable ways of arrangement of five girls such that Maggie and Lisa cannot stand next to each other = 120  48 = 72 ways Answer: option D
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 08 Jul 2012
Posts: 50

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
27 Jul 2015, 02:03
amod243 wrote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 Total ways (w/o restriction) 5 girls can be arranged in 5! ways = 120 Total ways in which Maggie and Lisa cannot stand next to each other = Total ways  total ways in which Maggie and Lisa stand next to each other = 120  (4!*2) = 120  48 = 72 ways. Ans. D, 72
_________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.  Thomas A. Edison



Intern
Joined: 05 Nov 2014
Posts: 41
Concentration: Marketing, International Business

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
27 Jul 2015, 05:42
GMATinsight wrote: Subanta wrote: can we solve this with \(P^n_r\) formula? Jut a personal Suggestion: It's best to see the steps and work in steps in P&C problems rather than being dependent on formulasHowever, Answer to your query is as follows Quote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 5 girls can stand in line in \(P^5_5 = 120 ways\) 5 girls can stand in line in such that Maggie and Lisa stand together in \(P^4_4 * P^2_2= 48 ways\) Total favourable ways of arrangement of five girls such that Maggie and Lisa cannot stand next to each other = 120  48 = 72 ways Answer: option D Thanks. I usually solve my problems without the formulae, but I have come across many problems where it is easier to use the formulae. I'm only trying to get familiar with the usage of the formulae.
_________________
Kudos = Thanks
"Yeah, you can get a nickel for boosting Starfall, but jacking Heal's a tenday stint in county. Now lifting Faerie Fire, they just let you go for that — it's not even worth the paperwork. But Reincarnation, man! That'll get you life!"



Senior Manager
Joined: 28 Jun 2015
Posts: 297
Concentration: Finance
GPA: 3.5

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
27 Jul 2015, 05:46
Five girls can stand in a line in 5! = 120 ways. Let M(Maggie) and L(Lisa) be treated as a single person ML. Now, ML can be placed in xxx any one of the 4 empty slots in 4! = 24 ways. ML can be ordered between themselves in 2! ways. So, the number of ways ML can stand together = 24 * 2 = 48. So, the number of ways they don't stand together is 120  48 = 72 ways. Ans (D).
_________________
I used to think the brain was the most important organ. Then I thought, look what’s telling me that.



Director
Joined: 23 Jan 2013
Posts: 596

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
22 Aug 2015, 21:57
Glue method (Maggie and Lisa stand together)
5!(4!*2)=72
D



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2442

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
29 Jan 2018, 11:13
amod243 wrote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 We can use the formula: Number of ways Maggie is not next to Lisa = total number of arrangements  number of ways Maggie is next to Lisa The total number of arrangements with no restrictions is 5! = 120. Maggie is next to Lisa can be shown as: [ML]  A  B  C Since Maggie and Lisa are now represented as one person, there are 4! ways to arrange the group and 2! ways to arrange Maggie and Lisa. Thus, we have 4! x 2! = 24 x 2 = 48 ways for Maggie to stand next to Lisa. Thus, the number of ways to arrange Maggie and Lisa such that they are not together is 120  48 = 72. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 27 Mar 2018
Posts: 11

In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
Updated on: 29 Mar 2018, 08:55
Hi Friends,
Can u anybody tell me how to solve this problem I am just bit modify this problem!
In how many ways can five girls stand in line if Maggie, Lisa, and Jane cannot stand next to each other?
Originally posted by VaibNop on 27 Mar 2018, 22:46.
Last edited by VaibNop on 29 Mar 2018, 08:55, edited 1 time in total.



Intern
Joined: 18 Dec 2017
Posts: 6

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
28 Mar 2018, 00:03
GMATinsight wrote: Subanta wrote: can we solve this with \(P^n_r\) formula? Jut a personal Suggestion: It's best to see the steps and work in steps in P&C problems rather than being dependent on formulasHowever, Answer to your query is as follows Quote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 5 girls can stand in line in \(P^5_5 = 120 ways\) 5 girls can stand in line in such that Maggie and Lisa stand together in \(P^4_4 * P^2_2= 48 ways\) Total favourable ways of arrangement of five girls such that Maggie and Lisa cannot stand next to each other = 120  48 = 72 ways Answer: option D Hi, your formulas, don't make any sense, you wrote them for n=k, please edit them. Thank you!



Director
Joined: 17 Dec 2012
Posts: 635
Location: India

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
28 Mar 2018, 21:50
amod243 wrote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 Leftmost arrangement of constraint elements is : M_L_ _ Using formula, we have number of permutations as 2!*3!*(3+2+1)=72 For explanation of the formula kindly see the link below.
_________________
Srinivasan Vaidyaraman Sravna http://www.sravnatestprep.com/bestonlinegrepreparation.php
Improve Intuition and Your Score Systematic Approaches



Director
Joined: 07 Dec 2014
Posts: 999

In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
29 Mar 2018, 00:03
amod243 wrote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 M & L can be separated in 6 ways, in these positions: 1 & 3 1 & 4 1 & 5 2 & 4 2 & 5 3 & 5 each of these 6 ways allows 12 possibilities: 2 for M & L: ML LM * 6 for the other 3 girls: ABC ACB BAC BCA CAB CBA 6*12=72 D



Intern
Joined: 27 Mar 2018
Posts: 11

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
29 Mar 2018, 08:57
gracie wrote: amod243 wrote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 M & L can be separated in 6 ways, in these positions: 1 & 3 1 & 4 1 & 5 2 & 4 2 & 5 3 & 5 each of these 6 ways allows 12 possibilities: 2 for M & L: ML LM * 6 for the other 3 girls: ABC ACB BAC BCA CAB CBA 6*12=72 D Hi Friends, Can u anybody tell me how to solve this problem I am just bit modify this problem! In how many ways can five girls stand in line if Maggie, Lisa, and Jane cannot stand next to each other?



Manager
Joined: 24 Aug 2016
Posts: 176
Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 540 Q49 V16 GMAT 2: 640 Q47 V31

Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]
Show Tags
16 May 2018, 04:28
VaibNop wrote: gracie wrote: amod243 wrote: In how many ways can five girls stand in line if Maggie and Lisa cannot stand next to each other?
(A) 112 (B) 96 (C) 84 (D) 72 (E) 60 M & L can be separated in 6 ways, in these positions: 1 & 3 1 & 4 1 & 5 2 & 4 2 & 5 3 & 5 each of these 6 ways allows 12 possibilities: 2 for M & L: ML LM * 6 for the other 3 girls: ABC ACB BAC BCA CAB CBA 6*12=72 D Hi Friends, Can anybody tell me how to solve this problem I am just bit modify this problem! In how many ways can five girls stand in line if Maggie, Lisa, and Jane cannot stand next to each other?Hello VaibNop , I have looked at your attempt. The same is ok to visualize but time consuming for exam. This is a problem of combinatorics. Lets understand when only 2 of the 5 can not stand side by side . then we will apply the logic in your query 3 of 5. Case 01: when only 2 of the 5 can not stand side by sideNow the total number of ways 5 people can be arranged =5P5=5!=120The Q asked in how many cases 2 can not stand side by side. Lets find the #cases where 2 can stand side by side . ( then, # ways when 2 donot stand side by side = total # ways 5 people stand  #cases where 2 can stand side by side) Lets assume these 2 are actually 1 object , hence our modified total = 4 objects. Now the total number of ways 4 objects can be arranged =4P4=4!=24.Now the 2 objects , which we considered to be a single object can be arranged among them selves in ways =2P2=2!=2 .#cases where 2 can stand side by side = 24*2 = 48Thus , # ways when 2 donot stand side by side = total # ways 5 people stand  #cases where 2 can stand side by side = 120  48 = 72 waysCase 02: when only 3 of the 5 can not stand side by side ....................Please note how we are just plugging in the values to our earlier understanding. Now the total number of ways 5 people can be arranged =5P5=5!=120The Q asked in how many cases 3 can not stand side by side.Lets assume these 3 are actually 1 object , hence our modified total = 3 objects. Now the total number of ways 3 objects can be arranged =3P3=3!=6.Now these 3 objects , which we considered to be a single object can be arranged among them selves in ways =3P3=3!=6 .#cases where 3 can stand side by side = 6*6 = 36Thus , # ways when 3 donot stand side by side = total # ways 5 people stand  #cases where 3 can stand side by side = 120  36 = 84 ways
_________________
Please let me know if I am going in wrong direction. Thanks in appreciation.




Re: In how many ways can five girls stand in line if Maggie and Lisa canno
[#permalink]
16 May 2018, 04:28






