M7MBA wrote: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
Good arrangements = total possible arrangements - bad arrangements.
Total arrangements:
Number of ways to arrange the 5 children = 5! = 120.
Bad arrangements:
In a bad arrangement, M and L stand next to each other.
To count the bad arrangements, put M and L in a BLOCK, as follows:
[ML].
Let the other 3 children be A, B and C.
Now count the number of ways to arrange the 4 elements [ML], A, B and C.
Number of ways to arrange the 4 elements [ML], A, B and C = 4! = 24.
Since [ML] can be reversed to [LM], the result above must be doubled:
2*24 = 48.
Good arrangements:
Total possible arrangements - bad arrangements = 120-48 = 72.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
