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

Question

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

Bunuel · Accepted Answer

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.

Gavan · Answer

thanks!

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

Please clarify.

Bunuel · Answer

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.

adiagr · Answer

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.

Ace800 · Answer

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!

delid · Answer

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 sub-group 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 sub-group, not on all of them. Hope it is clear...and correct!

ScottTargetTestPrep · Answer

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   as a single entity, and so we have:

- 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   in 3! = 6 ways.

So, the total number of ways to arrange the group is 720 x 6 = 4,320 ways.

Answer: D

Archit3110 · Answer

possible ways = 3! for 3 people and 6! for total group of 5 single + 1 of 3 people 
6*6! = 4320
IMOD

sachinsavailable · Answer

8 people if 3 have to sit together can be written as :

5+3= 6 (considering 3 as 1 batch)

6 people can sit together in 6! ways and 3 people (considered as 1 batch) can sit together in 3! ways.

total ways hence can be 6!x3!= 4320

Answer: C

Saiharish98 · Answer

Take 3 persons as a unit. So total of 6 persons. Six people can sit in 6! Ways. 3 people can rearrange themselves in 3! Ways. So 6! 3! Ways. So 720*6= 4320 ways. Hope you understood.

Posted from my mobile device

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards