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

Question

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

walker · Accepted Answer

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   and   are different.
4. Maggie and Lisa cannot stand next to each other in: 120 - 2*24 = 72 ways.

amod243 · Answer

Got it walker..

Thanks V.Much for this explanation

Subanta · Answer

can we solve this with  P^n_r  formula?

GMATinsight · Answer

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

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

JJo · Answer

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

Subanta · Answer

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.

TimeTraveller · Answer

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).

Temurkhon · Answer

Glue method (Maggie and Lisa stand together)

5!-(4!*2)=72

D

JeffTargetTestPrep · Answer

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:

- 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

VaibNop · Answer

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?

urbanoc · Answer

Hi,

your formulas, don't make any sense, you wrote them for n=k, please edit them. Thank you!

SVaidyaraman · Answer

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.

gracie · Answer

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

VaibNop · Answer

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?

u1983 · Answer

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 side

Now the total number of ways 5 people can be arranged  =5P5=5!=120 
The 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 = 48

Thus ,  # ways when 2 donot stand side by side = total # ways 5 people stand - #cases where 2 can stand side by side = 120 - 48 = 72 ways

Case 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!=120 
The 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 = 36

Thus ,  # 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

Archit3110 · Answer

total ways ; 5! = 120
and ML together ; 4! and adjacent 4!*2 = 48
so nor together ; 120-48 ; 72
IMO D

daniformic · Answer

I solved in this way:

+

is it wrong?

Thx

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards