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# Six friends go to see a comedy at the local movie theater and sit in a

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Math Expert
Joined: 02 Sep 2009
Posts: 60515
Six friends go to see a comedy at the local movie theater and sit in a  [#permalink]

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08 Apr 2016, 02:43
1
10
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:24) correct 40% (01:48) wrong based on 154 sessions

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Six friends go to see a comedy at the local movie theater and sit in a particular row together. If Grady and Howard are among those 6 friends but can never sit next to each other, how many 6-person seating arrangements are possible?

A. 360
B. 420
C. 480
D. 600
E. 720

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Manager
Joined: 09 Jul 2013
Posts: 107
Re: Six friends go to see a comedy at the local movie theater and sit in a  [#permalink]

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08 Apr 2016, 08:03
1
1
Ways to arrange 6 people in a row = 6! = 720

From this we want to subtract all the arrangements where Grady and Howard are next to each other. If we consider Grady and Howard one unit (GH), then the number of arrangements of the GH unit and the 4 other friends is 5! And the number of arrangements of G and H within the GH unit are 2 (GH or HG). So the total number of arrangements of the 6 friends with Grady and Howard together are 5!*2

Number of permutations where Grady and Howard are not seated next to each other = 6! - 5!*2 = 720-120*2 = 480

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Dave de Koos
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Joined: 24 Nov 2015
Posts: 475
Location: United States (LA)
Re: Six friends go to see a comedy at the local movie theater and sit in a  [#permalink]

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03 Jul 2016, 15:18
1
6 persons can be arranged in a row in 6! ways = 720 ways
consider Grady and Howard as 1 group in which they both sit together so we have 4 persons and 1 group
they can be arranged in 5! ways
Grady and Howard can arrange themselves in 2! ways
so in total the number of ways in which they are together is 5! * 2! = 120 * 2 = 240
subtract this number from total number of arrangements to get the number of arrangements in which Grady and Howard are not sitting together
720 - 240 = 480
Senior Manager
Joined: 23 Apr 2015
Posts: 274
Location: United States
WE: Engineering (Consulting)
Re: Six friends go to see a comedy at the local movie theater and sit in a  [#permalink]

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24 Aug 2016, 20:04
Bunuel wrote:
Six friends go to see a comedy at the local movie theater and sit in a particular row together. If Grady and Howard are among those 6 friends but can never sit next to each other, how many 6-person seating arrangements are possible?

A. 360
B. 420
C. 480
D. 600
E. 720

If Gary sits on one of the two corners, then Hardy will have 4 options, So 2(Gary's 2 corner) * 4(Hardy's 4 position) * 4!, the remaining 4 can have 4! arrangement,
And if Gary sits other than the corner, then Hardy will have only 3 options, So that is 4 * 3 * 4!

In total 2 * 4 * 4! + 4 *3 * 4! = 480.

+1 for kudos
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5700
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Six friends go to see a comedy at the local movie theater and sit in a  [#permalink]

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21 Nov 2019, 08:04
Bunuel wrote:
Six friends go to see a comedy at the local movie theater and sit in a particular row together. If Grady and Howard are among those 6 friends but can never sit next to each other, how many 6-person seating arrangements are possible?

A. 360
B. 420
C. 480
D. 600
E. 720

6 friends can sit in 6! ways and if 2 decide not to sit together ; 5! *2!
total ways ; 6!- ( 5!*2!) = 480
IMO C
Re: Six friends go to see a comedy at the local movie theater and sit in a   [#permalink] 21 Nov 2019, 08:04
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