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

## Sunday, June 14, 2009

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- Ariel Goldberg
- My name is Ariel Goldberg and I have been a GMAT tutor for eight years. I have taken the GMAT more than twenty times and scored into the 99th percentile; I like to share my GMAT knowledge with everybody. One of the things I like is to write GMAT quant questions that do reflect the changes in the test. The questions sold by some prep services are outdated in that they reflect the GMAT of three or four years ago, before Pearson took over. So that is where I come in, I provide people with good, real-looking GMAT questions.

5! - (4)(2!)(3!)= 72, right?

ReplyDeleteI agree that it's 72. A B C M L would be 5! without restrictions. Since M L can't be next to each other, you then need to subtract the 4*(3!) for whether (M L) is in the first, second, third or fourth position. In addition, multiply by 2! for L M versus M L.

ReplyDelete5! - 4*2!*31 = 72

ReplyDelete5!-2x(4!)=72

ReplyDeleteML can be considered one block-hence number of arrangements = 2x4! (M and L can be L and M)

Total number of arrangements 5!

The answer is A.

ReplyDeleteTotal number of ways without restrictions is 5!=120

Now just subtract the number of combinations where Lisa and Marie stand next to each other.

1 2 3 4 5

L M

L M

L M

L M

This is 4 combinations, now multiple by 4 by 2 since we can also do the opposite when Marie holds the first seat and Lisa the second.

4*2=8

Total Number of combinations possible given restriction= 120-8=112 => A

Anonymous, you are wrong, you forgot that movement of the other 3 people are also additional combinations, the answer is 72

ReplyDelete