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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. _________________

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, 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

However, 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. _________________

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"Yeah, you can get a nickel for boosting Starfall, but jacking Heal's a ten-day 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!"

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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