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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote In how many ways can you sit 8 people on a bench if 3 of the tagged by: rolandprowess This topic has 2 expert replies and 0 member replies In how many ways can you sit 8 people on a bench if 3 of the 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 Is there any strategic approach to this question? GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 ardz24 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 Is there any strategic approach to this question? This question could have been worded a little more clearly, but we'll take it to mean that there's enough room for all 8 people on the bench and that the 3 who wish to sit together does not change from scenario to scenario. Call the people A, B, C, D, E, F, G, H. Say A, B, and C insist on sitting together. If we fuse those people together, we now have A-B-C, D, E, F, G, H. In other words, we'll treat A-B-C as one entity. Along with A-B-C we have 5 more people to sit, so now we want to sit a total of six entities.. There are 6! or 720 ways we can do that. But now we have to recognize that A-B-C don't have to be seated so that A is farthest to the left andC is farthest to the right. They could sit B-A-C or C-B-A, etc. In fact, there are 3!, or 6 ways we can sit A, B, and C. 720 * 6 = 4320. The answer is D _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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ardz24 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

Letâ€™s say A, B, and C must sit together; we treat [A-B-C] 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.

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Jeffrey Miller
jeff@targettestprep.com

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