GMATD11 wrote:
A photo is being taken of Central High School's nine-member wrestling team. The team will stand in two rows, with the five shortest in the front row. The coach is also in the picture, in the middle of the back row. One of the taller boys is known to misbehave; to keep him from disrupting the photo session, he is placed next to the coach. How many possible arrangements of people are there for the photo?
A. 24
B. 30
C. 720
D. 1440
E. 2880
For the purposes of easiness i assign the letters to each type of people:
S - shorter guys
T - taller guys
M - misbehaving guy
C - coach
So our arrangements: for shorter guys is SSSSS = 5! is the total combination since the first guy could be put in 5 ways, second in 4, third in 3 etc. 5*4*3*2*1
In the back row we have two cases TMCTT and TTCMT in both cases CM are fixed because coach has to be in the center, so only other 3 T will be changing their places. There are 3 places for 3 T, so 3!=6.
Now we need to find the total number of combinations possible, we multiply 5! to 3! and we get 720. But considering that there are two possible ways for upper row we multiply the result by 2 and get 1440. Answer is D.