In how many ways can five girls stand in line...

[swerve]

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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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Hi swerve,

We're told that 5 girls are going to stand in a line. We're asked how many ways exist in which Maggie and Lisa DON'T stand next to each other.

If there were no 'restrictions' in terms of who could stand in which 'spot', then there would be 5! = 120 possible arrangements. However, since Maggie and Lisa cannot stand next to one another, we have to remove any of the permutations that would place them next to one another in line. There are a couple of different ways to calculate those arrangements. Here's one way that we can keep track of those options:

IF... Maggie and Lisa were the first two people in line, there would be...
M L 3 2 1 =6 possible arrangements
L M 3 2 1 =6 possible arrangements
12 arrangements that don't fit the restriction.

IF... Maggie and Lisa were the second and third people in line, there would be...
3 M L 2 1 =6 possible arrangements
3 L M 2 1 =6 possible arrangements
12 arrangements that don't fit the restriction.

This pattern will continue on (when Maggie and Lisa are the third/fourth and when they're fourth/fifth), so the total number of arrangements that don't fit are:
12+12+12+12 = 48 don't fit the restriction. Thus, 120 - 48 = 72 possible arrangements exist.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[GMATWisdom]

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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

THERE IS one convinient way:-
The total number of ways 5 girls can be arranged =5!=120
If Maggie and Lisa are clubbed as one girl then the number of ways =4!=24 with Lisa standing next to Maggie and 4!=24 ways when Maggie would stand next to Lisa.
Therefore there are 24+24=48 ways when Maggie and Lisa are together.
Number of ways when they are not together = 120-48=72
HENCE option D

[Scott@TargetTestPrep]

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

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.

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 standing next to Lisa can be shown as:

[M-L] - 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