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
