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# In how many ways can you seat 7 people on a bench if one of

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Intern
Status: Learning
Joined: 07 Aug 2011
Posts: 40

Kudos [?]: 49 [1], given: 10

Location: India
Schools: WBUT - Class of 2011
GMAT Date: 01-06-2014
GPA: 2.6
WE: Research (Education)
In how many ways can you seat 7 people on a bench if one of [#permalink]

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31 Oct 2013, 23:16
1
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00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:34) correct 24% (01:28) wrong based on 137 sessions

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In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080
[Reveal] Spoiler: OA

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Arindam Sur

Last edited by arindamsur on 01 Nov 2013, 01:02, edited 2 times in total.

Kudos [?]: 49 [1], given: 10

Math Expert
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128752 [1], given: 12182

Re: In how many ways can you seat 7 people on a bench if one of [#permalink]

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01 Nov 2013, 00:43
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Expert's post
arindamsur wrote:
In how many ways can you seat 7 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?

A) 720
B) 1720
C) 2880
D) 5040
E) 10080

Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 4 chairs to sit. The remaining 6 people can sit in 6! ways. Thus the # of arrangements is 4*6! = 2,880.

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Kudos [?]: 128752 [1], given: 12182

Current Student
Joined: 17 Sep 2013
Posts: 24

Kudos [?]: 14 [0], given: 1

Location: United States
Concentration: Economics, Statistics
Schools: CBS '18 (M)
GMAT 1: 770 Q51 V45
GPA: 3.36
WE: Analyst (Health Care)
Re: In how many ways can you seat 7 people on a bench if one of [#permalink]

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01 Nov 2013, 09:48
There are 7! total ways to sit everyone.

There are 3 seats that he can't sit in (the two ends and the middle). For each seat of the 3 seats he can't sit in, there are 6! arrangements of people in the other seats. So the total number of arrangements where he isn't sitting in any of those three seats is:

7! - 6!(3) =
6!(7 - 3) =
6!(4) =
2880

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Intern
Status: Bring it on.....!
Joined: 11 Jul 2013
Posts: 31

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Location: India
Concentration: Technology
GMAT 1: 660 Q49 V31
Re: In how many ways can you seat 7 people on a bench if one of [#permalink]

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02 Nov 2013, 01:42
total no of ways in which all 7 can be seated = 7! ways

now,
if rohit sits at first seat then remaining 6 can be seated in 6! ways
if rohit sits at middle seat then remaining 6 can be seated in 6! ways
if rohit sits at last seat then remaining 6 can be seated in 6! ways

no. of ways in which rohit doesnt sits in middle or at either ends = 7! - (6! + 6! + 6!) = 7! - 6!*3 = 6!(7-3)=6!*4=2880

Hope this helps.
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Live as if your were to die tomorrow. Learn as if you were to live forever - Gandhi

Kudos [?]: 19 [0], given: 9

Re: In how many ways can you seat 7 people on a bench if one of   [#permalink] 02 Nov 2013, 01:42
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