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Counting - seating 7 people

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 31, 2009 8:43 am

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.

Last edited by Brent@GMATPrepNow on Sat Jan 31, 2009 9:00 am, edited 1 time in total.

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Source: Beat The GMAT — Problem Solving | Sat Jan 31, 2009 8:43 am

aroon7: Master | Next Rank: 500 Posts; Posts: 160; Joined: Sat Dec 20, 2008 9:12 pm; Thanked: 11 times

by aroon7 » Sat Jan 31, 2009 8:50 am

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

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by Brent@GMATPrepNow » Sat Jan 31, 2009 9:01 am

aroon7 wrote: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

Last edited by Brent@GMATPrepNow on Sat Jan 31, 2009 9:09 am, edited 1 time in total.

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aroon7: Master | Next Rank: 500 Posts; Posts: 160; Joined: Sat Dec 20, 2008 9:12 pm; Thanked: 11 times

by aroon7 » Sat Jan 31, 2009 9:05 am

Brent Hanneson wrote:
aroon7 wrote: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...

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Jan 31, 2009 9:08 am

Right you are.
The answer is E.

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aroon7: Master | Next Rank: 500 Posts; Posts: 160; Joined: Sat Dec 20, 2008 9:12 pm; Thanked: 11 times

by aroon7 » Sat Jan 31, 2009 9:10 am

Brent Hanneson wrote: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.

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ontopofit: Senior | Next Rank: 100 Posts; Posts: 68; Joined: Sun Dec 21, 2008 12:00 am; Thanked: 3 times

by ontopofit » Sat Jan 31, 2009 11:50 am

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.

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vikram_k51: Master | Next Rank: 500 Posts; Posts: 208; Joined: Sat Jan 31, 2009 11:32 am; Location: Mumbai; Thanked: 2 times

Re: Counting - seating 7 people

by vikram_k51 » Sat Jan 31, 2009 12:05 pm

Brent Hanneson wrote: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

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