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# In how many ways can you sit 8 people on a bench if 3 of

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Intern
Joined: 20 Nov 2011
Posts: 37

Kudos [?]: 37 [1], given: 5

GMAT Date: 05-28-2012
GPA: 3.23
WE: Engineering (Computer Software)
In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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12 Mar 2012, 09:23
1
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2
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25% (medium)

Question Stats:

63% (00:49) correct 37% (00:47) wrong based on 178 sessions

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In how many ways can you sit 8 people on a bench if 3 of them must sit together?

A. 720
B. 2,160
C. 2,400
D. 4,320
E. 40,320
[Reveal] Spoiler: OA

Kudos [?]: 37 [1], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41699

Kudos [?]: 124810 [4], given: 12079

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12 Mar 2012, 09:35
4
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Expert's post
Gavan wrote:
In how many ways can you sit 8 people on a bench if 3 of them must sit together?
a) 720
b) 2,160
c) 2,400
d) 4,320
e) 40,320

i'm getting 'e' but that is not OA

Say 8 people are {A, B, C, D, E, F, G, H} and A, B and C must sit together. Consider them as one unit {ABC}, so we'll have total of 6 units: {ABC}, {D}, {E}, {F}, {G}, {H}, which can be arranged in 6! ways. Now, A, B and C within their unit can be arranged in 3! ways, which gives total of 6!*3!=4,320 different arrangements.

Hope it's clear.
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Kudos [?]: 124810 [4], given: 12079

Intern
Joined: 20 Nov 2011
Posts: 37

Kudos [?]: 37 [0], given: 5

GMAT Date: 05-28-2012
GPA: 3.23
WE: Engineering (Computer Software)
Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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12 Mar 2012, 09:59
thanks!

did you consider following arrangements?
1: -{D},{ABC}, {E}, {F}, {G}, {H},
2: -{D},{E}, {F},{ABC}, {G}, {H},
3: -
..

Kudos [?]: 37 [0], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41699

Kudos [?]: 124810 [1], given: 12079

Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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12 Mar 2012, 10:30
1
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Expert's post
Gavan wrote:
thanks!

did you consider following arrangements?
1: -{D},{ABC}, {E}, {F}, {G}, {H},
2: -{D},{E}, {F},{ABC}, {G}, {H},
3: -
..

6 distinct object can be arranged in 6! different ways, so 6 units {ABC}, {D}, {E}, {F}, {G}, {H} can be arranged in 6! different ways, which takes cares of all possible cases.

Check Combinations chapter of Math Book for more: math-combinatorics-87345.html

Hope it helps.
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Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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23 Feb 2014, 18:16
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Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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29 May 2016, 22:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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29 May 2016, 23:57
Gavan wrote:
In how many ways can you sit 8 people on a bench if 3 of them must sit together?

A. 720
B. 2,160
C. 2,400
D. 4,320
E. 40,320

In such questions, always tie the person that have to sit together. So we have effectively 5+"1" = 6 "persons" to arrange.
They can be arranged in 6! ways.
Now the 3 persons can themselves be arranged in 3! ways.

Total ways: 6!*3! = 4320.

Kudos [?]: 135 [0], given: 9

Re: In how many ways can you sit 8 people on a bench if 3 of   [#permalink] 29 May 2016, 23:57
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