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# Probability question

Author Message
Intern
Joined: 15 Oct 2017
Posts: 28
Schools: Northeastern '20

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06 Mar 2018, 22:25
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 1 sessions

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Hello guys,

sometimes I struggle with that type of question.

Q : If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?

A : 72. Without limitations, 5 children can be seated in 5!=120 ways. Find the number of ways to seat the 5 children so that the siblings DO sit together. The siblings can be regarded as one unit so there are 4! combinations. But within this unit the siblings can sit in two different ways. So the number of ways to seat the 5 children so that the siblings DO sit together is 4!∗2=48. Thus, the number of combinations in which the siblings DO NOT sit together is 120 - 48 = 72.

So If the question was If among 5 children there are 3 siblings, the answer will be 120-(4!∗3), am I right?

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Math Expert
Joined: 02 Sep 2009
Posts: 52370

### Show Tags

06 Mar 2018, 22:43
thegame12 wrote:
Hello guys,

sometimes I struggle with that type of question.

Q : If among 5 children there are 2 siblings, in how many ways can the children be seated in a row so that the siblings do not sit together?

A : 72. Without limitations, 5 children can be seated in 5!=120 ways. Find the number of ways to seat the 5 children so that the siblings DO sit together. The siblings can be regarded as one unit so there are 4! combinations. But within this unit the siblings can sit in two different ways. So the number of ways to seat the 5 children so that the siblings DO sit together is 4!∗2=48. Thus, the number of combinations in which the siblings DO NOT sit together is 120 - 48 = 72.

So If the question was If among 5 children there are 3 siblings, the answer will be 120-(4!∗3), am I right?

Discussed here: m08-183801.html

Check other Arrangements in a Row and around a Table questions in our Special Questions Directory.

21. Combinatorics/Counting Methods

For more:
ALL YOU NEED FOR QUANT ! ! !

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: Probability question &nbs [#permalink] 06 Mar 2018, 22:43
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