Quant Exam > Quant Questions > P and Q are sitting in a ring with 11 other p...
Start Learning for Free
P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?
- a)1/3
- b)1/4
- c)1/5
- d)1/6
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
P and Q are sitting in a ring with 11 other persons. If the arrangemen...
Fix the position of P, then Q can be sit in 12 positions, so total possible outcome = 12
Now, exactly 4 persons are sitting between them. This can be done in two ways as shown in figure, so favourable outcomes = 2
So, probability = 2/12 = 1/6
Most Upvoted Answer
P and Q are sitting in a ring with 11 other persons. If the arrangemen...
Problem: P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?
Solution:
Total Number of ways of arranging 13 persons in a ring = (13-1)! = 12!
Let P be fixed. Then, we have to arrange Q and 4 persons out of remaining 11 persons in between P.
Number of ways of selecting 4 persons out of 11 persons = 11C4
Number of ways of arranging 4 persons in between P and Q = (4-1)! = 3!
Number of ways of arranging P, Q, and 4 selected persons = 6 (as P and Q can be arranged in 2! ways)
Therefore, the total number of ways of arranging P, Q, and 4 persons in between them = 11C4 x 3! x 6
Now, if we fix both P and Q, then we have to arrange remaining 7 persons.
Number of ways of arranging 7 persons = 7!
Therefore, the total number of ways of arranging P, Q, and 4 persons in between them with 7 persons arranged in remaining seats = 11C4 x 3! x 6 x 7!
Thus, the required probability = (11C4 x 3! x 6)/12! = 1/6
Hence, the correct option is D.
Solution:
Total Number of ways of arranging 13 persons in a ring = (13-1)! = 12!
Let P be fixed. Then, we have to arrange Q and 4 persons out of remaining 11 persons in between P.
Number of ways of selecting 4 persons out of 11 persons = 11C4
Number of ways of arranging 4 persons in between P and Q = (4-1)! = 3!
Number of ways of arranging P, Q, and 4 selected persons = 6 (as P and Q can be arranged in 2! ways)
Therefore, the total number of ways of arranging P, Q, and 4 persons in between them = 11C4 x 3! x 6
Now, if we fix both P and Q, then we have to arrange remaining 7 persons.
Number of ways of arranging 7 persons = 7!
Therefore, the total number of ways of arranging P, Q, and 4 persons in between them with 7 persons arranged in remaining seats = 11C4 x 3! x 6 x 7!
Thus, the required probability = (11C4 x 3! x 6)/12! = 1/6
Hence, the correct option is D.
Free Test
FREE
| Start Free Test |
Community Answer
P and Q are sitting in a ring with 11 other persons. If the arrangemen...
Fix the position of P, then Q can be sit in 12 positions, so total possible outcome = 12
Now, exactly 4 persons are sitting between them. This can be done in two ways as
shown in figure, so favourable outcomes = 2
So, probability = 2/12 = 1/6
Now, exactly 4 persons are sitting between them. This can be done in two ways as
shown in figure, so favourable outcomes = 2
So, probability = 2/12 = 1/6
|
Explore Courses for Quant exam
|
|
Similar Quant Doubts
P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer?
Question Description
P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
Download more important topics, notes, lectures and mock test series for Quant Exam by signing up for free.
Here you can find the meaning of P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice P and Q are sitting in a ring with 11 other persons. If the arrangement of 11 persons is at random, then the probability that there are exactly 4 persons between them?a)1/3b)1/4c)1/5d)1/6e)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Quant tests.
|
|
Explore Courses for Quant exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup