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

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Joined: 20 Nov 2011
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GMAT Date: 05-28-2012
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In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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12 Mar 2012, 08:23
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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
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Kudos [?]: 93280 [4] , given: 10555

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12 Mar 2012, 08:35
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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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Re: In how many ways can you sit 8 people on a bench if 3 of [#permalink]

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12 Mar 2012, 08:59
thanks!

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

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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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12 Mar 2012, 09:30
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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, 17:16
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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, 21:54
Hello from the GMAT Club BumpBot!

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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, 22:57
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.

Re: In how many ways can you sit 8 people on a bench if 3 of   [#permalink] 29 May 2016, 22:57
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