TEST 38 #10

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dunkin77: Master | Next Rank: 500 Posts; Posts: 269; Joined: Sun Apr 01, 2007 5:41 am

TEST 38 #10

by dunkin77 » Tue May 01, 2007 1:58 am

10. The president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?
(A) 4
(B) 5
(C) 20
(D) 24
(E) 120

Hi,
I thought the answer was E) by doing 5P4 but the answer is D) ... Can you help?

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Source: Beat The GMAT — Problem Solving | Tue May 01, 2007 1:58 am

Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 am; Thanked: 5 times; Followed by:2 members

by Cybermusings » Tue May 01, 2007 8:54 am

Fix the president in the middle chair

Other 4 people can be arranged in 4*3*2*1 = 24 ways

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bww: Senior | Next Rank: 100 Posts; Posts: 55; Joined: Sun Apr 29, 2007 6:25 am; Location: MA; Thanked: 1 times

by bww » Wed May 02, 2007 5:36 pm

hey there...can someone help? so in the case above you used 4! or n!, right? isn't n! when you must choose from a set of n objects from the source to fill specific spots when order matters?

so when would you use n!/(n-r)! ?

thx!

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mschling52: Master | Next Rank: 500 Posts; Posts: 105; Joined: Mon Sep 18, 2006 12:34 pm; Location: OH; Thanked: 7 times; GMAT Score:780

by mschling52 » Thu May 03, 2007 5:06 am

I believe the permutation formula you refer to still holds in this case. We have four spots to fill and four people to fill them, so

nPr = n!/(n-r)!

4P4 = 4!/(4-4)! = 4!/0! = 4! = 24

since 0! is defined to be 1.

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ns88: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Sat Apr 14, 2007 8:29 am

by ns88 » Sat May 05, 2007 10:25 am

Whenever there’s a question that involves that two people must sit together, or one person has to sit somewhere specifically, treat it as one person. Thus five becomes four factorial.

If all five people can sit anyway they want, then 5!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Dec 12, 2017 6:22 am

dunkin77 wrote:10. The president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?
(A) 4
(B) 5
(C) 20
(D) 24
(E) 120

We are given that we must arrange 5 people in a row; however, the president MUST BE seated in the center chair. Since the president's seat is already determined, we need to arrange 4 people, which can be done in 4! = 24 ways.

Answer: D

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