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# In how many ways can five girls stand in line if Maggie and Lisa canno

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Manager
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In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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05 Feb 2010, 13:18
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58% (01:44) correct 42% (00:52) wrong based on 58 sessions

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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
[Reveal] Spoiler: OA

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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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05 Feb 2010, 13:31
1
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Expert's post
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.
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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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05 Feb 2010, 13:52
Got it walker..

Thanks V.Much for this explanation
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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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27 Jul 2015, 00:09
can we solve this with $$P^n_r$$ formula?
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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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27 Jul 2015, 01:19
Expert's post
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 formulas

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

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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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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
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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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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 formulas

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

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.
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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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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 -x-x-x- 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).
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Re: In how many ways can five girls stand in line if Maggie and Lisa canno [#permalink]

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22 Aug 2015, 21:57
Glue method (Maggie and Lisa stand together)

5!-(4!*2)=72

D
Re: In how many ways can five girls stand in line if Maggie and Lisa canno   [#permalink] 22 Aug 2015, 21:57
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