Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Nov 2011
Posts: 33
Concentration: Marketing, International Business
GMAT Date: 05282012
GPA: 3.23
WE: Engineering (Computer Software)

In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
12 Mar 2012, 09:23
Question Stats:
61% (01:03) correct 39% (01:22) wrong based on 247 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59722

Re: Combinations
[#permalink]
Show Tags
12 Mar 2012, 09:35
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. Answer: D. Hope it's clear.
_________________




Intern
Joined: 20 Nov 2011
Posts: 33
Concentration: Marketing, International Business
GMAT Date: 05282012
GPA: 3.23
WE: Engineering (Computer Software)

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



Math Expert
Joined: 02 Sep 2009
Posts: 59722

Re: In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
12 Mar 2012, 10:30
Gavan wrote: thanks!
did you consider following arrangements? 1: {D},{ABC}, {E}, {F}, {G}, {H}, 2: {D},{E}, {F},{ABC}, {G}, {H}, 3:  ..
Please clarify. 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: mathcombinatorics87345.htmlHope it helps.
_________________



Manager
Joined: 18 Jan 2010
Posts: 238

Re: In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
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. D is the answer.



Intern
Joined: 30 Aug 2017
Posts: 13
Concentration: Real Estate, Operations

Re: In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
24 Oct 2017, 08:35
Bunuel wrote: 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. Answer: D. Hope it's clear. quick question regarding this: Since the question doesn't specify which 3 people need to sit together, how come we don't have find ways of choosing 3 ppl out of the 8 to act as unit? Like {DEF}, {AGF} etc etc.. I was thinking we would have to do 8C3 x 3! x 6!... can you tell me where I am going wrong with my logic? Thanks for your help!



Intern
Joined: 07 Jul 2017
Posts: 9

In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
29 Oct 2017, 12:20
Ace800 wrote: Bunuel wrote: 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. Answer: D. Hope it's clear. quick question regarding this: Since the question doesn't specify which 3 people need to sit together, how come we don't have find ways of choosing 3 ppl out of the 8 to act as unit? Like {DEF}, {AGF} etc etc.. I was thinking we would have to do 8C3 x 3! x 6!... can you tell me where I am going wrong with my logic? Thanks for your help! I'll try to give you my interpretation, waiting for some math expert Choosing 3 people out of 8, you would calculate all the possible subgroup of 3 people you could select from a group of 8. E.g., ABC, ABD, ABE, BCD, FGH, FBE, ... so on so forth. The question specify "if 3 of them must sit together". Therefore it is not asking to find all the possible combinations in which 3 people can always sit next to each other. Paraphrasing, it is just asking "no matter who, consider that there are 3 people that decided they must always sit together (either ABC or ABD or ABE etc..): in this case, how many combinations can we create?" . That is why you have to do your calculation only on one possible subgroup, not on all of them. Hope it is clear...and correct!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8692
Location: United States (CA)

Re: In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
31 Oct 2017, 16:40
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 Since we are not given any names, we can denote each person with a letter: A, B, C, D, E, F, G, H Let’s say A, B, and C must sit together; we treat [ABC] as a single entity, and so we have: [A  B  C]  D  E  F  G  H We see that we have 6 total positions, which can be arranged in 6! = 720 ways. We also can organize [A  B  C] in 3! = 6 ways. So, the total number of ways to arrange the group is 720 x 6 = 4,320 ways. Answer: D
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5479
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)

Re: In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
Show Tags
23 Nov 2019, 09:27
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 possible ways = 3! for 3 people and 6! for total group of 5 single + 1 of 3 people 6*6! = 4320 IMOD




Re: In how many ways can you sit 8 people on a bench if 3 of
[#permalink]
23 Nov 2019, 09:27






