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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?
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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.
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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
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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?
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