Counting - seating 7 people

[Brent@GMATPrepNow]

In how many ways can Al, Bea, Clyde, Dawn, Ed, Faye and Gina be seated so that there are exactly two people seated between Al and Bea?

A) 240
B) 360
C) 480
D) 600
E) 960

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

[aroon7]

ans is E

we need

A X X B X X X
X can be occupied by others
A = Al
B = Bea

we can shift the arrangement A X X B four times:

A X X B X X X
X A X X B X X
X X A X X B X
X X X A X X B

and other places can be occupied by 5*4*3*2*1 = 120

so total arrangements = 4*120 = 480

[Brent@GMATPrepNow]

ans is E

we need

A X X B X X X
X can be occupied by others
A = Al
B = Bea

we can shift the arrangement A X X B four times:

A X X B X X X
X A X X B X X
X X A X X B X
X X X A X X B

and other places can be occupied by 5*4*3*2*1 = 120

so total arrangements = 4*120 = 480

Sorry, aroon7 - my original set of answer choices were incorrect (I have since changed them on the original post).
The answer isn't 480

[aroon7]

ans is E

we need

A X X B X X X
X can be occupied by others
A = Al
B = Bea

we can shift the arrangement A X X B four times:

A X X B X X X
X A X X B X X
X X A X X B X
X X X A X X B

and other places can be occupied by 5*4*3*2*1 = 120

so total arrangements = 4*120 = 480

Sorry, aroon7 - my original set of answer choices were incorrect.
The answer isn't 480

Still I vote for E (this time 960)

we can switch the places of A and B
so, we should multiply 480 by 2 to get 960...

[Brent@GMATPrepNow]

Right you are.
The answer is E.

[aroon7]

Right you are.
The answer is E.

This is what I calculated before... but since I didnt find the answer choice, i thought 'between A and B" would mean A comes before B...
Thanks for the question Bernt.

[ontopofit]

I did in some diff fashion
if we consider A _ _ B a single word,we can arrange 4 letters in 4! ways.
Now A abd B can be interchanged.So it becomes 2*4!
We can select 2 letters b/w A and B, and arrange them in 5P2 ways (20)
hence the answer is 2*4!*20 = 960.
I think my approach is not as gud as aroon's.I would prefer ur approach.

[vikram_k51]

In how many ways can Al, Bea, Clyde, Dawn, Ed, Faye and Gina be seated so that there are exactly two people seated between Al and Bea?

A) 240
B) 360
C) 480
D) 600
E) 960

Please note that this is not an official GMAT question; it’s my attempt to create difficult (650+ level) GMAT-style questions for this forum.

A)240

A12B. The 2 places b/w A,B can be filled in 5 ways and these 2 ppl can sit in 5*2 ways. A and B can arrange in2 ways thus 5*2*2 ways.the other 3 can arrange in a 3 ways,thus 5*2*2*3.

Considerind A,B and the other 2 as 1 and the entire block as 4 units the total is: 5*2*2*3*4=240