GRE® question: Permutation problem

[Abhi_86]

HI
i want to know the method to solve this problem.it appears in the math review section of powerprep software.

please help me out

Martha invited 4 friends to go with her to the movies. There are 120 different
ways in which they can sit together in a row. In how many of those ways is
Martha sitting in the middle?

the answer given is 24.
but i think the answer is 72.

total no of ways in which they can be seated is 120.
no of ways in which martha is in the corner seat is 24+24(at either end).
therefore the answer should be 120-48 = 72 according to me.

thanks.

[Mister Micawber]

.
Sorry, I'm no good at math. Got a grammar question?
.
_________________
Native English teacher at Mister Micawber's

[Peekaboo]

1) She invited 4 friends, so there are 5 of them.
To confirm this you are given the number 120

Permutation of 5*4*3*2*1= 120

So 4 friends and Mary always in the middle, you can diligently write out all the 24 different way..if M = Mary and her friends are ABCD, You can write

AB M CD
BA M CD
BA M DC
AB M DC
CD M AB

Keep going, you should get 24...time waster huh

OR you can simply think of it this way ...these approach is on 800score.com

5 places : _ _ M _ _

You have 4 people filling up those spaces beside Mary
There first place you have a possible of 4 people who can fill that space, Second space you now have 3 people, on the other side of Mary, you have the 3 space, and 2 people choose from and finally one space to one person

therefore you have

4 3 M 2 1

Multiply all these together you get 4*3*2*1 = 24

Just sheer logic...If you can do the math approach just use logic in permutation problems as in writing every frigging thing out!!

[Peekaboo]

1) She invited 4 friends, so there are 5 of them.
To confirm this you are given the number 120

Permutation of 5*4*3*2*1= 120

So 4 friends and Mary always in the middle, you can diligently write out all the 24 different way..if M = Mary and her friends are ABCD, You can write

AB M CD
BA M CD
BA M DC
AB M DC
CD M AB

Keep going, you should get 24...time waster huh

OR you can simply think of it this way ...these approach is on 800score.com

5 places : _ _ M _ _

You have 4 people filling up those spaces beside Mary
There first place you have a possible of 4 people who can fill that space, Second space you now have 3 people, on the other side of Mary, you have the third space, and 2 people choose from and finally one and only one possible person to occupy that space

therefore you have

4 3 M 2 1

Multiply all these together you get 4*3*2*1 = 24

Just sheer logic...If you can do the math approach just use logic in permutation problems as in writing every frigging thing out!!

[Abhi_86]

sorry . i misunderstood the problem. i thought middle means any position in between 2 people. i dint think it meant exactly in the middle of the row.
anyway thanks for clearing the confusion.

[Peekaboo]

well I interpreted it that way in order to solve. it..But I just understood what you meant and its quite possible..One of the interesting thing about practicising this test and also LEARNING THE LANGUAGE..because regular folks like us will understood thing differently but ETS has it LANGUAGE..in the most part they try to be unequivocal as much as possible.

You can try using your idea and the permutations explanation above to see if you get the same answer, on the otherhand, someone might have a diferent explanation for it...you will probably come across it in Kaplan or any of the other ones or just google the questions and you might hit on someone who explained it elsewhere...there are folks on Yahoo Answers devoted to explaining GRE maths problems..

[Avinash Meda]

martha can sit in the middle...so fix the position....if martha has to be in the middle then there are remaining 4 positions which can be filled by four others in 4! =24 ways