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# Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They

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Joined: 28 Jun 2018
Posts: 130
Location: Bouvet Island
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Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They  [#permalink]

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19 Jan 2019, 02:36
1
4
00:00

Difficulty:

45% (medium)

Question Stats:

50% (01:13) correct 50% (01:32) wrong based on 42 sessions

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Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They are seated in a line while taking the exam together. What is the probability that Ron and Charles are not sitting together?

(A) 1/3
(B) 1/8
(C) 1/12
(D) 1/2
(E) 1/4
Math Expert
Joined: 02 Aug 2009
Posts: 7959
Re: Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They  [#permalink]

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19 Jan 2019, 05:11
2
1
blitzkriegxX wrote:
Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They are seated in a line while taking the exam together. What is the probability that Ron and Charles are not sitting together?

(A) 1/3
(B) 1/8
(C) 1/12
(D) 1/2
(E) 1/4

You can make 4! arrangements with 4 people= 4!=24.
Now take two of them, R and C, as 1, so now there are 3 of them B, K, and (RC), and they can be arranged in 3! ways. Also each of this 3! ways can be made in 2 ways - RC or CR. Thus, 2*3!=12
so ways R and C are not sitting together is 24-12=12 and the probability is 12/24=1/2

D
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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India
Re: Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They  [#permalink]

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19 Jan 2019, 05:13
2
blitzkriegxX wrote:
Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They are seated in a line while taking the exam together. What is the probability that Ron and Charles are not sitting together?

(A) 1/3
(B) 1/8
(C) 1/12
(D) 1/2
(E) 1/4

So here is Karishma's solution

The best way to solve a "not sitting together" question is to make them sit together.

Total ways of 4 people sitting together = 4! = 24
No of ways in which 2 will sit together = 3!*2! (arrange 3 people/groups in 3! ways and the two people together can be arranged in 2! ways) = 12
No of ways in which they will not sit together = 24 - 12 = 12

Required Probability = 12/24 = 1/2

Check this post for more: https://www.veritasprep.com/blog/2011/1 ... ts-part-i/
_________________
Karishma
Veritas Prep GMAT Instructor

Re: Charles , Bunuel , Ron and Karishma are appearing for the GMAT. They   [#permalink] 19 Jan 2019, 05:13
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